United saw their crown snatched away from them by Manchester City in the dying seconds of the last campaign via their 3-2 win over QPR with two last-gasp goals.
Carrick admits it took time to get over that blow but expects a positive response and believes the arrival of Robin van Persie from Arsenal provides a massive boost ahead of the opening clash at Everton on Monday evening.
"What happened takes some getting over. It's not easy. It was a huge blow, the way it happened," he said.
"Nobody could have predicted that and we never thought it was going to happen like that.
"But we have to get over it now. We've had setbacks in the past and we have to move on. That's the nature of the club and the manager. He'll be driving us forward to achieve something this season.
"As a club we do tend to bounce back. If we have a defeat or setback we tend to come back stronger. We can't forget how close we were. It wasn't a disaster in terms of how the season went because we had a good season really.
"We'll bounce back. We're strong this year and we're hungry, not that we wouldn't have been hungry anyway. It will be a good championship."
Carrick revealed the pre-season message from Sir Alex Ferguson was the same as always.
"It was just 'go again'. Whether we won the league last season or not it's the same, the same message really," he said.
"He says 'you have to start again, start afresh. Last season doesn't count for anything now, everything is new' and we'll look forward to it."
In terms of bringing Van Persie to Old Trafford, Carrick said: "It's great news. We want the best players in the club.
"It's been well publicised that we've been chasing him and it's a big boost for us. It's a big week now going into the first game of the season and it will give everyone a big lift."
On a personal level, Carrick ended his self-imposed England exile by returning for the mid-week friendly international with Italy in Berne and he skippered the side for the final 20 minutes.
"It was special to be back. I hadn't played for over two years for England," he said.
"In terms of not playing, I went to the last World Cup and I was there but was never going to play - and I knew that. There were injuries in midfield and I still didn't get a look in.
"It was getting to the stage where I was always turning up and not playing. I decided if I wasn't close to being involved, I'd rather not be there.
"It wasn't a case of 'play me or I quit' because if anyone knows me, they'll know that's not me at all.
"Then obviously Fabio (Capello) left and Roy (Hodgson) came in and there was maybe a little bit of confusion over that.
"But I have to drawn a line under that really and moved on and being captain at the end on Wednesday was a special moment, an extra-special moment.
"It's one of them things that happened and something I'll remember forever."