The Channel Tunnel operator has asked to be reimbursed more than £22m (29m euros). It made a pre-tax profit of £89m (115m euros) in 2015.
It faced serious disruption from migrants trying to cross the Channel.
Revealing its annual results, the company said there had been no disruption to services since October.
Spokesman John Keefe said: "The French and British governments are clearly responsible for the security at the border, and also for the public order security on site.
"During last year we were severely disrupted by the migrant crisis - people trying to break on to our terminal and break into trucks on the motorway - and so we suffered quite a loss of revenue during the early part of the year."
At the height of the problems during the summer, about 2,000 migrants a night were trying to get into the Coquelles terminal, causing Eurotunnel to suspend many of its services.
Border security at the terminal was strengthened later in the year.
Charlie Elphicke, the Conservative MP for Dover and Deal, said it was "quite shameless of Eurotunnel to try and present the British government and the French government with this bill".
"Their profits have rocketed and everyone knows that the British government has invested tens of millions of pounds making the border stronger, safer and more secure," he said.
Eurotunnel is seeking millions of pounds in compensation from the UK and French governments because of revenue lost during the Calais migrant crisis.