"You have to give credit to Barcelona," Evra told uefa.com.
"For the moment we have to accept that for the last four years Barcelona have been the best team in the world, and United the second."
United had hoped they could rely on the experience they have gained over the past few seasons, when they have secured four Premier League titles in five years.
However, it soon became apparent that the Barcelona players' knowledge of each other is so much more intense.
"We know each other, but they know each other so well, so perfectly," said Evra.
"Every time Messi gets the ball he knows Xavi is going to be there, Pedro is going to be there, or (Andres) Iniesta.
"It was very difficult, Barcelona keep the ball really well."