United had looked set to chalk up a third straight win in all competitions before Diego Costa's late equaliser salvaged a point for the Blues at Stamford Bridge.
That result left the Red Devils six points behind fourth-placed Manchester City and 12 behind leaders Leicester in the Barclays Premier League, and t hey are out of the Champions League.
They are in Europa League and FA Cup action this month alongside the continued top-flight battle, though.
And United midfielder Carrick told manutd.com: "There is plenty to play for this month and of course plenty of points to play for in the league.
"We're not giving anything up just yet. I think it (Sunday) was a big day for us in terms of the league situation. If we'd have gone there and got a win we'd have been in good shape, but it wasn't to be and it makes things harder for us.
"It's hard to take, losing two points so late on. I know we were under pressure for the last 10 or 15 minutes but to lose a goal like that is disappointing and that's the overall feeling.
"I thought we played well and produced some really good football. We looked dangerous going forward and defended well for most of the game. We just didn't do the right things at the right time near the end and see the game out.
"We have to battle on though, keep going and play something like we have been doing over the last few weeks and then see where that takes us."
Source: PA