Regarding the contest, veteran midfielder Carrick was happy to pick up a point as United look to force their way into the top four by season's end.
"It's a point gained for us," Carrick told Sky Sports.
"We thought we could catch City on the break and we did have a couple of chances but overall I thought we did well except at the end when there was a bit of excitement.
"It makes things more difficult when you go down to 10 men."
United remain fifth on the Premier League table on 64 points, one behind fourth-placed City, with five fixtures remaining in 2016/17.