"This is a bad day for Europe, it risks undermining the position of national governments," Cameron said after EU leaders voted 26-2 for the former Luxembourg premier to replace Jose Manuel Barroso.
Asked if Britain was closer to an exit from the 28-member bloc as a result, Cameron said: "The job has got harder of keeping Britain in a reformed European Union... Do I think it's an impossible job? No."
But for Britain to get its way on Europe "it is going to be a long, tough fight and frankly sometimes you have to be willing to lose a battle to win a war," Cameron said.
Cameron forced an unprecedented vote on the Juncker nomination at a high-stakes Brussels summit despite having the support of only Hungary among the other 27 EU members.
With the fight now over, leaders are expected to try and appease Cameron, potentially by offering London a top job in Brussels, but the dispute threatens to fuel eurosceptic sentiment in Britain ahead of a referendum on EU membership, to be held in 2017 if Cameron's Conservatives win next year's general election.