He said if Scots voted to leave the UK, they would no longer benefit from the rebate Britain receives from the European Union (EU) - and would even have to pay towards this.
Scotland would receive less money from the EU's structural fund programme, according to Mr Alexander.
While he said the amount of funding an independent Scotland would receive from Europe's Common Agricultural Policy (Cap) could increase, he also warned money from this source could fall by just over £1 billion.
Even if an independent Scotland received an extra £850 million in Cap money - as the Scottish Government states - Mr Alexander argued the country would still be worse off overall.
He went on to claim if Scotland were to vote Yes in the referendum, its membership of the EU would be under "entirely different" terms from Britain - which has obtained opt-outs on joining both the euro and the Schengen area, in which people can travel between countries without showing passports.
Mr Alexander spoke out as he visited Glasgow with Foreign Secretary William Hague to launch the latest of a series of papers from the UK Government looking at the potential impact of independence.
That paper argued the "most optimistic" case was that Scotland would be £1.9 billion worse off as an independent member of the EU over the period 2014 to 2020 - but that could rise to £3.8 billion "under less optimistic scenarios".
Mr Alexander said: "What this means for Scottish families is that over the next seven years, continuing as part of the United Kingdom will save them at least £750 per household, possibly climbing to £1,470 per household.
"So, as part of the UK we Scots pay less, and we get more out of our EU membership."
He said: "On our EU membership alone, Scotland would be between £1.9 billion and £3.8 billion better off as part of the UK over the next seven years."
Over the period 2014 to 2020, Scotland would lose about £200 million in EU structural funds if it was independent, Mr Alexander claimed.
The Chief Secretary to the Treasury said: "On Cap payments the picture is more complex. But in the best-case scenario - incidentally the only scenario put forward by the Scottish Government - Cap payments would increase by £850 million over the seven years.
"In the worst case scenario Cap payments would in fact decrease by over £1 billion."
He added what was "most important" was the UK's "unique" EU rebate, which is worth about £3 billion a year.
Mr Alexander said: "The Scottish Government's position is that the UK's rebate can simply be shared in the event of independence.
"But that's not how a rebate works. It's not an annual lump sum that can be divided."
He said for an independent Scotland to get such a rebate "there would have to be a change to the rule book approved by every other single EU member state".
This, he said, would be "unprecedented", adding: "No other country has ever secured any budgetary correction on joining the EU.
"So, it is inconceivable that an independent Scotland would secure a rebate as the UK has."
He also stated as all new EU member states contribute to the UK rebate, an independent Scotland would have to do this too - adding this could cost Scotland nearly £600 million over the seven-year period.
Mr Alexander insisted: "The bottom line is this - Scotland outside of the UK would have to negotiate its own way back into the European Union, and as such its terms of membership would be entirely different to those we currently enjoy.
"Scotland would be a net contributor to the EU, it would pay more than it would get back."
The report, the latest in a series of papers from the UK Government, focuses on the EU and international issues.
As it was published, Mr Hague cast doubt on claims from the Scottish Government that the country would enjoy a "seamless transition" to EU membership.
In the foreword to the Scottish Government's independence white paper, Deputy First Minister Nicola Sturgeon recognised EU membership would require negotiations with other member states and institutions, but said this could be done from within the organisation in the period between a Yes vote in September and Scotland becoming a new state in March 2016.
The white paper also argues it is wrong to say Scotland would have to leave the EU and reapply from outside, stressing Scotland has been an integral part of the EU for 40 years.
But Mr Hague said it was "not reasonable for the Scottish Government to expect what they have claimed would be a 'seamless transition'".
He also insisted there were question marks over whether an independent Scotland would have to agree to join the euro and the Schengen zone.
Mr Hague said new members of the EU were required to commit to both of these - saying only Denmark and the UK had a permanent opt-out on the euro, while only the UK and Ireland had negotiated a similar opt-out from the Schengen area.
"It is clear that all new member states for many years have been required to make the legal and political commitment to joining the euro," he said.
Mr Hague claimed there would be "immense issues to be discussed" in negotiations for an independent Scotland to join the EU.
He also cast doubt on whether these talks could be completed within the 18 months between the referendum and Scotland potentially becoming an new state
The Foreign Secretary said: "I've been in a lot of European negotiations and in all my experience they take much longer than anybody ever forecasts, and here you are talking about negotiations with these huge issues that Scotland doesn't want to join the euro but that is the rule for new members.
"I've never seen anything of that complexity resolved in 18 months - it takes years and years for new member states to be able to negotiate membership of the European Union normally."
He insisted that being in the UK gave Scotland the "opportunity to do more good in the world" and to "exert an influence on global politics or economies".
He went on: "It gives the security of belonging to a nation of 63 million people, with one of the fastest-growing economies in the developed world and a tried and trusted defence and security network which is the envy of many other nations and will help to keep the Commonwealth Games secure this summer.
"It also guarantees a British passport, which provides instant access to our extensive diplomatic, consular and trade networks and the most professional help worldwide for any Scot travelling or doing business overseas."
Mr Hague said there would be "great risks" if Scotland opted to end the union, adding: "Making a decision to remain within the United Kingdom is a positive choice, reinforcing what we already have and reaffirming what more we can be if we continue to work together."