United saw the Premier League crown snatched from their grasp in dramatic fashion last season, with Manchester City stealing it away with virtually the last kick of the campaign.
Only goal difference separated Manchester's arch-rivals in the final reckoning, and it looks like being another tight chase this time around.
United are aware of the need to avoid a repeat of last season's heartache and are determined to build on the lead they have been able to open up at the top of the table.
Carrick told The Sun: "We're in a good position but if we don't keep doing the right things we know what can happen.
"It's not a case of being more determined this time. We would be hungry to win the league regardless of what happened last year.
"We were hurting in the summer. It wasn't a nice thing that we went through on the last day. But it's gone now, we've got to focus on what is ahead of us.
"We know City are not going to go away but there are so many games left that if you spend too much time thinking about who is getting what result, it can drive you mad. We just have to keep winning matches."
Next up for United is a trip to Carrick's former employers Tottenham, and the England man is hoping he can maintain his high standards at White Hart Lane.
Carrick added: "I'm happy with the way things are going, but I'm not getting carried away. People are saying nice things but I'm just doing the same things I've done since I've been here.
"If that ends up as a good season for me, then great.
"But it's not so much my own form, it's about winning things. We're still going on three fronts and it's a big few weeks for us - but I'm sure we'll be saying that for the rest of the season."
Tottenham v Manchester Utd is live on Sky Sports 1 this Sunday. For more details click here.