The response came as US Secretary of State John Kerry and his Russian counterpart Sergey Lavrov last night held hastily convened talks in Paris, building on discussions between their countries' leaders about ways to resolve the dispute.
Mr Hammond said he hoped a diplomatic solution could be found but that it was important to maintain pressure on Moscow following its use of "very crude" tactics against its neighbour.
The Defence Secretary said there were concerns about Russian troops on the border with Ukraine, following the annexation of the Crimean peninsula.
He said UK forces were stepping up their involvement in military exercises in eastern Europe to provide reassurance for Nato members in the region that they would be defended in the event of any Russian attempts to violate their territory.
Russia has annexed Crimea and there have been reports of thousands of Russian troops massed close to Ukraine's borders.
Earlier Mr Lavrov set out demands for a neutral and federal Ukraine, an idea Kiev called "full capitulation".
However, Mr Lavrov has categorically denied any plans for an invasion.
Mr Hammond said: "Everybody is concerned. We are concerned that there might be a further incursion in the territory of a sovereign nation.
"Whether there is or there isn't, we all need to be concerned about the use of this very crude and blunt instrument to try to influence other countries and their behaviour.
"We thought we had seen the end of that kind of thing in Europe."
He added: "Certainly one of the things we are looking at is a greater participation in exercises in the Baltic States, the eastern European Nato member countries, as a way of reassuring them about our commitment to Article 5 of the Washington Treaty, the mutual guarantee."
Article 5 means an attack on one Nato nation is viewed as an act of aggression against them all.
The talks between Mr Kerry and Mr Lavrov follow a telephone conversation between US president Barack Obama and Russian premier Vladimir Putin.
Mr Obama urged Mr Putin to withdraw his troops from the border with Ukraine.
The Russian leader, who initiated the call, asserted that Ukraine's government was allowing extremists to intimidate civilians with impunity - something Ukraine insists has not happened.
Asked about the possibility of a breakthrough, Mr Hammond said: "I hope so, because we have to find a diplomatic solution to the crisis over the Crimea while continuing to make very clear to the Russians that if they were to go any further into the Ukraine there would be a raft of new measures against them which would seriously hurt the Russian economy."
Meanwhile Russia has set out demands for a diplomatic resolution to the crisis in Ukraine, saying the former Soviet republic should be unified in a federation allowing wide autonomy to its various regions.
In Paris, Mr Kerry sat down with Mr Lavrov at the residence of the Russian ambassador to France after a brief call on French foreign minister Laurent Fabius.
The pair were due to go over Moscow's response to and American plan to de-escalate the situation.