The Red Devils briefly returned to the top of the table after Sunday's 2-0 win over QPR at Loftus Road, before rivals Manchester City responded with a 1-0 victory against Arsenal at the Etihad Stadium.
Carrick, who scored United's second goal to confirm the three points returned to Old Trafford, insists the players are looking strong and is happy to see the club in the hunt for a 20th top-flight crown.
"People have been writing us off but we are looking strong and we are happy with the way we are going," said Carrick. "There is still a long way to go."
United's shock elimination from both the UEFA Champions League and the Carling Cup had led to suggestions of a crisis, but Carrick insists it is anything but, and is adamant that Sir Alex Ferguson's side are in confident mood.
Reflecting on his strike against Rangers - a fine solo effort which ended a barren run of 70 games and almost two years without a goal - the 30-year-old midfielder revealed he was satisfied with the end result.
"The last time I scored a goal from inside my own half was probably when I was playing Under 12s," he added. "It just seemed to open up for me and I kept on going and going and thought 'why not?'
"It was great to see it go in. It seemed to take forever to actually reach the back of the net. It wasn't a relief getting my first for so long, I was more interested in killing the game off."