United, who are now 14 points off the pace in the Premier League table, go into Wednesday's match at Old Trafford on the back of a 2-1 first-leg defeat at the Stadium of Light.
But Carrick said: "Times have been difficult. Performances have not been that bad actually but results have been pretty awful for us to take.
"We are giving everything at the minute but it's just not going our way. If we all stick together, I am sure it will turn soon.
"We want to play again as quickly as possible and Wednesday is another big game.
"It is an opportunity to get to a final. You can't take that lightly and the fans have been unbelievable over the last month or so especially."
As for boosting their Champions League chances for next season, the experienced midfielder added: "We never give up. We will keep fighting. That is what we do.
"We still believe. We have to try and win as many games as we can and see where it takes us."