United lost eight times last term – including two defeats to Chelsea and losses at Liverpool and relegated Burnley – yet still only lost their Premier League crown by a single point.
Tonight, the Red Devils open their quest to reclaim the championship against Newcastle at Old Trafford, already playing catch-up on Chelsea, who registered a 6-0 win over West Brom. Carrick feels any ground lost in the early weeks might prove hard to make up.
"The way it looks, you cannot afford to drop too many points," said the midfielder.
"Last season was a bit of a freak in terms of how many games both us and Chelsea lost and how many points were dropped.
"The previous few years there wasn't much margin for error and competition is pretty fierce again now. Teams who have finished around the Champions League places are looking to break through and you really have to start firing from the off."
The sheer weight of Manchester City's spending marks them out as a big danger, whilst Carrick also feels Liverpool will be striving hard to make their mark under new boss Roy Hodgson after last season's difficulties.
Yet Carrick still views Chelsea as the team to beat, last season's Double triumph demanding greater respect.
"Chelsea are the champions, so you have to put them right up there," said the 29-year-old.
"You have to respect what they have in the squad and what they have achieved over a number of years now."