The 31-year-old midfielder grabbed the only goal in Wednesday night's encounter at Old Trafford and then quickly turned his attention to the clash with the Reds.
Carrick told reporters: "Everyone has got a huge responsibility to respect the situation. Hopefully the football will be celebrated as it is one of the classic football games worldwide.
“These games are a one-off, form goes out of the window, the atmosphere is that little bit more special. We are expecting Liverpool to bring their best game and we'll have to bring ours.
"To play in a game like that, they are the ones you remember. As a player you appreciate what it means to the fans.
“Anyone who's been to one - at Old Trafford or Anfield - the atmosphere is a bit special and hopefully the game can live up to it."
The midfielder also reflected on a rare goal – his first of the season – and what it meant to secure a positive start to another European campaign.
He added: "I don't get many [goals]. People say [I should get more], but the position dictates that. You look at other defensive midfielders around Europe and they don't necessarily score more goals.
“Of course in an ideal world I'd like to score more, but I'm not really around the box that much.
"We wanted to start well, give ourselves a good chance to win the game, we knew they were a good side. It's just disappointing we didn't kick on from there. Three points was huge for us today.
"It's important to win our home games but it's equally important to go away and try and win those games."
During the game, former Germany international Dietmar Hamann described Carrick as "the best holding midfielder in England by a country mile".
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"He [Carrick] is the best holding midfielder England got by a country mile."