"It was by far not a classic," Carrick told MUTV. "Obviously we weren't at our best and the flowing football that you want to play and the chances that you want to create didn't quite happen. But we got a clean sheet which was quite pleasing and I thought we defended well.
"They had a couple of opportunities and when they put balls into the box like they did, those can fall to anybody. But overall I thought we defended well - we didn't play as well as we could have but we won the game and managed to keep a clean sheet.
"A clean sheet is the biggest plus that we can take from tonight. They pumped a lot of balls into the box, asked questions and made us defend. Our two centre halves were terrific. West Ham had two big guys - as Carroll goes off, Carlton Cole comes on - and it can be tough.
"But we got the clean sheet. It is something to build on because the performance needs to be better. A second goal would've put us in a much better position going into the final few minutes but, in the end, we held on and we're still in a good position at the top of the league. We are quite satisfied."