Rooney’s two-goal haul, which included his 200th strike as a Manchester United player, inspired the Reds to get their Group A campaign off to a perfect start with a 4-2 victory.
Robin van Persie was also in sublime form, volleying United into a 2-1 lead when he hooked home a cross from Antonio Valencia, and all three players were praised to the hilt by an impressed Carrick.
“It was probably Wayne's best performance that I've seen for a while,” the midfielder told ManUtd.com. “It's great to have him in that form - he can be untouchable when he’s like that.
“To have lads like that in your team is brilliant. I thought Antonio was immense on Tuesday night as well and to have Wayne and Robin scoring and assisting is fantastic. Even if they're maybe not having the best of games they can always come up with something. I thought they played really well on Tuesday.”
Carrick is convinced that the team have found form at the right time ahead of Sunday's derby.
“I don't think we've played that badly so far this season,” he added. “The Swansea game was a good game, the Chelsea one was tight, but Liverpool is always a bit of a one-off game which you can't really read too much into.
“We won at the weekend, and on Tuesday we took it to another level and improved again. Hopefully we can do it again on Sunday. The performance will breed confidence, and we'll have to do it all again on Sunday.”