United striker Michael Owen scored the winner in the 96th minute, despite the fourth official only indicating four extra minutes.
“You’re disappointed to lose any game – Craig scored two wonder goals for us and we thought we’d done enough to get a point, but it wasn’t to be,” Lescott told the club’s official website.
“There are no excuses. We are pros and we have to look at ourselves collectively and as individuals and realise that it just wasn’t good enough.
“We look at each other and we’ve made mistakes. We started the season with four clean sheets and now we’ve conceded goals. We have to correct that.
“Last-minute goals are hard to take. We are gutted to lose as we did. Maybe we showed a bit of naivety towards the end. We’re not a side to sit back. We want to win every game but sometimes you have to realise you can’t.
“A lot was made of this game beforehand, but you can’t come to Old Trafford, concede four goals, and expect to get anything. We’ll have to work on that in the week.
“Their fans didn’t go home thinking it was an easy game. We put them under a lot of pressure today and if we’d got the draw it would have been fully deserved.
“We believe in ourselves and we believe that we can push for honours this season. Arsenal came here and lost too. We still believe we can finish in the top four.”