The midfielder scored the only goal of a tense triumph over the Turkish champions, and the efficient manner in which United closed out the victory hinted at a growing maturity in a side whose inexperience was so ruthlessly exposed in European competition last season.
"It's vital we got off to a winning start after last year, really," Carrick told Sky Sports. "It was vital we won at home, especially against a good team - and they really are a very decent team.
"They kept possession very well. At times I thought we defended well, especially in the second half when we limited them to possession without really hurting us. That was a good sign for us.
"They counter-attacked on us quite well and were a bit of a threat, but we nullified that in the second half and overall we can be happy; we've played some good stuff and we've won the game."