Centre-back Coloccini played his first game since February 24 and the result was a clean sheet and a point at West Ham.
The 0-0 draw through leaves United in a scrap to avoid relegation, and they have a vital match against QPR - already down - next weekend before hosting Arsenal on the last day of the season.
"I think it helped us because we know Coloccini's a good player with a lot of experience," midfielder Tiote said.
"He played well and I'm happy to see him back because we're going to need him for the next two games.
"I think we deserved more than the one point because, when you see the game, I felt we wanted it more than West Ham.
"We missed some chances and we didn't score the goal we needed but we need to take the positives and think about the next game."
"We need to win," he said. "Before the [West Ham] game we knew we had to win or take one point, but we could not lose. We have one point and that's important.
"Everyone was together and we played as a team. We were more compact and that's important.
"On Sunday we've got to do the same and hopefully we can take the three points."