Nicola Sturgeon also defended Mr Salmond's line on currency, under which an independent Scotland would enter into a currency union with the rest of the UK. Her intervention followed media claims that senior figures within the party were unhappy with their leader's performance on Tuesday night.
Defending Mr Salmond, Ms Sturgeon said: "We have made the rational case for a currency union and the arguments are absolutely solid, that this is best for Scotland and best for the rest of the UK."
Emphatically denying that there was disunity in the party in the wake of the televised debate, she said: "All of us in the SNP came into politics for Scotland to become a normal country in control of its own affairs. The mood in the party has never been better and belief is sky high. When we look at the polling after the debate, Alex Salmond winning over undecided voters and women voters was hugely encouraging.
"For those debates to be effective they must not be aimed at politicians and pundits but at ordinary voters."
Her comments came as the First Minister came under fresh pressure from leading economist Dr Angus Armstrong of the National Institute for Economic and Social Research, who warned an independent Scotland would struggle to bail out crisis-hit banks if it chose to use the pound without a formal currency-sharing deal with the remainder of the UK, a process known as sterlingisation.
Meanwhile, more than 200 celebrities and public figures have urged Scotland to stay part of the UK ahead of the country's historic vote on independence.
Sir Mick Jagger, Sir Bruce Forsyth, Dame Judi Dench, Simon Cowell and Professor Stephen Hawking are among the famous names to sign an open letter to "voters of Scotland" in the build-up to next month's referendum.