"We created a lot of chances in the game and it was a match that we should have won," Fletcher told MUTV. "We played good attacking football but unfortunately you've got to put away the chances to win matches.
"We didn't take our chances and we could have lost it when they hit the post. We were fortunate in that respect, but the only positive is that we're creating those chances and eventually they're going to go in."
Chelsea are the Reds' next opponents on Sunday and, while Fletcher admits it has been a stop-start to the defence of the Double, he insists United are aiming for victory at Stamford Bridge.
"It's been a bit like that," he said. "We've had a few injuries and suspensions, but now we've got everyone back, which is good. It (Sunday) is a massive game already.
"Obviously after losing to Liverpool we can't lose too much ground in the Premier League. Chelsea have got a great record at home, and it's something that we're looking to end. We're looking to win the match and get up the league.
"Everyone's back now, we're looking to kick on, win the match and hopefully that'll start a run of them."