United lost 1-0 to the Blues at Stamford Bridge on Monday to bow out of the competition following the 2-2 draw at Old Trafford in March and the Frenchman was disappointed at not being able to make amends for the clubs shortcomings in the Champions League.
"We were really sad to lose in the Champions League - this game hurt us a lot when we lost against (Real) Madrid," Evra told ITV.
"We really wanted to win the double and for a lot of players, even myself, we haven't won the FA Cup. It was an important trophy."
He added: "Now we're going to focus on the league. It's nearly done. We have to win a few games."