Southampton, who continually pumped the ball forward in search on an unexpected point at the Theatre of Dreams.
In the end, the Reds defended admirably and although fans were forced to endure a nervy climax, Carrick is convinced the result was rarely in doubt - citing the fact that De Gea had very few saves to make against the spirited Saints.
“To be honest, I thought we defended well, it was my mistake that led to their goal and you can’t really legislate for that, it wasn’t really a defensive error in terms of the team,” Carrick noted.
“I thought we looked quite solid when defending the goal, David had the free kick to save and apart from that he didn’t have an awful lot else. It’s just one of those things.
“We are delighted with the three points, we knew it was a big game and it was a terrific result for us. People will look at it and think we shouldn’t be too happy because we haven’t played well.
“But Southampton have improved of late and we knew it would be a tough game. We can improve on the performance and I’m sure we will do that on Saturday. We are happy with the three points.”