Sir Alex Ferguson's side edged to victory in a 4-3 thriller against Reading on Saturday but the midfielder was disappointed with his side's defensive display.
Carrick told the Manchester Evening News: "That's the standards we set; we're not happy until we know we're playing to our potential. The pleasing thing is there's a lot more to come from us.
"There's a lot more room for improvement in certain aspects of our play but at the same time we're sitting on top of the league and we've won again.
"We can't get too down about things, there are a lot of positives."
|5/6||Manchester United are 5/6 with William Hill to win the 2012-13 Premier League|
Although United showcased defensive frailties, the England international maintained that he always had faith in their ability to come back, explaining: "Even if we do go a goal down we always feel we've got the firepower from different people.
"That's the strength in depth of the attacking options and that's what keeps driving us on and we never give up.
"Personally I always felt confident, even when we were going goals behind, that we could still get back in the game and win the game, and that obviously proved the case."