The home side twice took the lead but were unable to hold on for three points as Nani and Michael Owen gave United a point.
Defender Zat Knight told ESPN: "It's very disappointing when you twice go up at home, I think we deserved to win the game.
"Johan (Elmander) had a good chance right at the end, it wasn't to be but the boys stuck at it.
"It's massive point for us, a few teams we feel are going to be around us at the end of the season won yesterday so we wanted to get a result today."
Martin Petrov was equally disappointed, adding: "Especially when we score 20 minutes from the end of course we are disappointed we didn't win, but we showed we can play with quality against good teams and that is very important for us."
Owen, who came off the bench to score his 200th career goal, said: "It's always a tough place to come but we created enough chances and dominated most of the game but we're disappointed to only get a point.
"With the results this weekend it was an opportunity to close that gap at the top but it wasn't to be and we have to focus on our next game now.
"We were helped with a few nice resutls yesterday but when you don't capitalise fully it's disappointing. It's a long season and we'll bounce back."
United manager Sir Alex Ferguson felt a draw was a fair result, adding: "In the first half we should have done better but we did well to come from behind.
"The second half was very even. Bolton were a real handful and our chances were reduced but we must take credit for coming back again, it shows a bit of character.
"I think a lot of teams coming here will find it very difficult. I thought it was a fair result."
Asked about failing to capitalise on Saturday's results, Ferguson added: "Teams drop points when we don't expect them.
"Away from home we've scored seven goals and only got three points, it's a very difficult league."
Ryan Giggs and Wayne Rooney were both substituted in the second half and Ferguson added: "Ryan is the most serious, it's a hamstring and I'm afraid he will be out for a couple of weeks.
"I'm sure Wayne will get ready for Wednesday."
Bolton boss Owen Coyle added on ESPN: "I felt having led twice we had opportunities to see the game through, but there were many pleasing aspects today, we looked fresh and energetic.
"I thought the performance was outstanding. There is a tinge of disappointment but I'm very pleased with how the lads went about it.
"You have to start well against teams of the calibre of Manchester United and we did that."