Berbatov scored his 14th league goal of the season at Birmingham but United were pegged back by Lee Bowyer's controversial last-gasp equaliser.
Bulgarian striker Berbatov finished off a slick piece of play by the Red Devils and Carrick said: 'It was a good move and a terrific finish by Berba. His confidence in front of goal is very high at the moment and hopefully that continues for a long time.
Hammered home: Berbatov (right) scores United's goal at Birmingham
'His goal put us in a great position but if we had done better with a couple more opportunities on the counter-attack then we would have been a lot happier.'
Sir Alex Ferguson's side finish 2010 at the top of the table but Carrick still feels hard done by over Bowyer's goal at St Andrew's.
The midfielder pounced on Nikola Zigic's knock down but the big striker appeared to foul Rio Ferdinand and handle the ball amid suspicions of offside.
Carrick added on MUTV: 'We were certainly down when we came off the pitch. Late goals are always hard to take but given how it happened we feel hard done by.
Frustrated: Carrick was left to rue Bowyer's late leveller at St Andrew's
'There was a push in the back and then obviously the handball. But it's done now, so we have to dust ourselves down and move on.
'We're still in a good position when you look at the bigger picture. We haven't lost, we're in good form - we played well at times, controlling the game - and so we go into the next game looking to keep the momentum up.'
United travel to face West Bromwich on Saturday afternoon.
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