Carrick frustrated by Man Utd's lack of sharpness in West Ham draw
Carrick's side were well below their best for long periods in east London and trailed to Tomas Soucek's 50th minute strike.
United needed Benjamin Sesko's equaliser deep into stoppage-time to avoid the first defeat of Carrick's five-match reign as interim manager.
Although United retained fourth place in the Premier League thanks to Sesko's dramatic leveller, Carrick conceded there was a lack of cohesive play in the final third from his team.
"I think we were a little disappointed and we were definitely not at our best. It's times like that when you find a way and move on. I'm a little frustrated at that," he said.
"It is a tough place to come and we didn't have that sharpness to find the answers. Great spirit again and we will take the point and move on.
"For where we are and being together for a short space of time, in the end we have to take a point.
"It didn't come easy and we found a way. We will take some positives from it."
Sesko's fifth goal in his last six games maintained his recent improvement after a woeful start to his first season at United following his move from Leipzig.
"Fantastic finish. He has done it again. It is important. It is a great finish. Delighted for him. Another big goal and a good step," Carrick said.
United's late escape left West Ham stuck in the relegation zone.
Carrick hopes his former club can eventually climb away from the bottom three.
"I would love them to stay up," he said. "It was a big part of my life and I have great memories here so hopefully they stay up."