The hosts started brightly with Chicharito opening the scoring after four minutes with a well-placed header, before Wayne Rooney doubled United's lead with a free kick that eluded the Chelsea defence, soon after.
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"We were delighted with the way we started and maybe took our foot off the gas in terms of the penetration and going forward,” Carrick told talkSPORT.
"Their first goal changes a lot of things and after that it was scrappy from us."
The draw on Sunday capped a disappointing week for United after being eliminated from the Champions League last Tuesday following defeat to Real Madrid.
But Carrick, who played in both games, said the defeat to Madrid was not an excuse for Sunday’s poor performance.
"It's been a tough week," the 31-year-old added. "Playing at this club [that] is not an excuse though."
The replay will take place at Stamford Bridge in the coming weeks but the midfielder says United need to concentrate on their Premier League fixture at home to Reading on Saturday.
He said: "There's a lot of positives, it's not the end of the world. We just need to regroup and start again Saturday."