"Scoring doesn't really mean much because we lost, we're all desperately disappointed," he told MUTV. "We never got going and didn't create the chances we normally do. That's not like us. It was good to see that the minute's silence was well observed. But in terms of the game we're not going home happy."
City took the lead midway through the first half through Darius Vassell, with Benjani Mwaruwari grabbing a second just before the interval.
"Once City got the two goals it was hard to come back from it," added Carrick. "They set out their game plan and it worked for them. One goal down, you always believe you've got a chance of coming back, but two is difficult. We needed to score right after half time to give us momentum, but when we did score it was too little, too late."
Arsenal could move five points clear if they beat Blackburn at the Emirates Stadium on Monday, but Carrick firmly believes the Gunners will slip up before the end of the campaign.
"There are still games to play," he said. "I don't think Arsenal will go the rest of the season without dropping points. If they did, fair play to them. There are still going to be ups and downs in the title race, and hopefully there will be more ups for us and we can overtake them."