The £18.5 million buy from Spurs in 2006 has won at least one piece of major silverware in each of his three seasons so far at Old Trafford.
And Carrick admits that, despite the shock of the Leeds defeat, United's trophy-winning ambitions for the new year remain unaltered.
He said: 'Our first aim in 2010 is to win the league again. It's always been the first thing we've set out to do and to win four in a row would be amazing.
'Then there's the Champions League. Given how tough it is to be successful, our record over the last few years has been very good.
'We also want to do well in the Carling Cup. We want to get our hands on as much as possible.
'This season has been strange with some odd results, but it's a vital time and the manager has stressed that to us, although most of us have been here before.
'We know how important it is. It's always three more vital points or the next round of a cup, so every game becomes more important.'
United goalkeeper Ben Foster is aiming for a recall against City after missing a chance of a rare start against Leeds due to a virus.
The England international has not played since the 1-0 Champions League defeat against Besiktas last November due to the form of Tomasz Kuszczak, but Foster admits he is desperate to return to action.
He said: 'Tomasz has come in and done really well, but hopefully I'll get a few games soon.
'As well some important league games, we've got big cup matches coming up against City in the Carling Cup.
'People will talk about the last derby game in the build-up, but I'm not sure how much bearing it'll have on the tie.
'That result (4-3 to United) will have hurt City and they'll want revenge, but the bottom line is City always want to beat us, and we want to beat them!
'Hopefully we will produce a good performance we'd love to go to a final again because we want to defend the trophy, and getting to Wembley gives everyone a boost.'