Vidic admits tiredness may have played a part during the first half, but says the Reds should be buoyed by their response after the restart.
"We were more aggressive and pressed higher up the pitch after half-time and that had an affect on the game," he told MUTV.
"We had some good half chances and if the final ball had been better we could maybe have been celebrating at the end.
"We still have five games to play and we need to win all of them. It won't be easy, but the second half against Chelsea gives us hope that we can do well."
He added: "We hope there will be more dropped points from our rivals and Chelsea do at least have the FA Cup to think about as well as the league.
"If we win our last five games I think we'll have a good chance."