The Red Devils face Galatasaray in Istanbul on Tuesday having secured qualification from their group with two games to spare.
Now, Carrick is looking forward to travelling abroad to take on some of Europe's finest clubs at their home stadiums.
"That is the big test," Carrick told reporters. "That is when the competition really comes alive.
| MANCHESTER UNITED LATEST
|9/1||Manchester United are 9/1 to win the Champions League with bet365
"We have done the first part. The second one is when we get the really big European nights and we go away to the best places in Europe and win games.
"We have managed to do that very well over the past few years. Hopefully we can get back to that."
Carrick insisted, however, that he would not dedicate any time to thinking about who United might face in the last 16 according to the results of the final two rounds of group stage fixtures.
"You can drive yourself mad thinking about who you might get and all the various permutations," he added.
"We just have to win our games, which we have done, and see what the draw gives us. Whoever it is, we will be ready in February."
The England international admitted that there was a better atmosphere around the club because of their success in Europe in 2012-13 compared to the difficulties they experienced in both the Champions League and the Europa League last season.
"It is a happier place because of what we are doing in the Champions League," he revealed. "Last year we were chasing our tails a bit and came up short. This year we have been ahead of the game.
"Getting those wins and points on the board makes it an awful lot easier."