United, who face mid-table Swindon Town at Bramall Lane this afternoon, trail sixth-placed Peterborough United by a single point - but sit 12 behind Walsall in second.
And with 20 games to go, defender Collins said: “Every single one means something now.
“Once you turn the corner at the halfway stage, everyone has something to really play for - be it relegation, play-offs or automatic promotion.
“Very seldom is there a team out of both and People start to feel the pressure. Sir Alex Ferguson called it ‘squeaky bum time’. When you are playing someone fighting relegation, you’re chasing promotion, it makes it a tense affair.
“In August or September everyone still their dreams of having a fantastic season.
“Now it’s down to the nitty gritty.”
United put the disappointment of their FA Cup tie at Old Trafford, which saw Manchester United progress courtesy of Wayne Rooney’s 93rd-minute penalty, behind them to seal a battling point at Wigan - after being 3-0 down - and then beat Colchester with a late winner.
“It was a very tough week. We have gone to Old Trafford, given everything, and should have got a replay,” Collins added.
“We didn’t, so you have the psychological blow of that - plus the physical fatigue - and went to Wigan, a really strange game where I don’t think we deserved to be 3-0 down.
“But we pulled it back, showed unbelievable characteristics in the team, and we were all very pleased to come away with a point.
“Then going down to Colchester and winning, it ended up being a really good week. The only disappointment was not getting the replay from Manchester United, but there were a lot of positives to take.”