The Red Devils took the lead in the 37th minute through Henrikh Mkhitaryan, enjoyed 64% of possession and mustered 16 shots, seven of which were on target, throughout the game.
Carrick told BT Sport: "It's frustrating. We were so in control but got sloppy, we have to kill teams off. We should have won that game.
"They had one chance and scored a header. We need to be more ruthless, it's as simple as that. We were too comfortable. We got sloppy.
"It's not the end of the world but we are better than that. It's that little edge that makes the difference in the end, but we'll look forward to the next game."
The return leg takes place on Thursday, April 20 at Old Trafford.