The 31-year-old midfielder grabbed the only goal in Wednesday night's encounter at Old Trafford and though he was satisfied with the club's start to their European campaign, Carrick chose to preview a "classic" Premier League match-up.
Carrick told reporters: "Everyone's got a huge responsibility to respect the situation. Hopefully the football will be celebrated as it's one of the classic football games worldwide.
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"To play in a game like that, they're 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 the group stage.
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.
Meanwhile, 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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Although Carrick played the full 90 minutes against the Azzurri, he did not start in either of the qualifying clashes and Hamann - who scored the final goal at the old Wembley Stadium for Germany in 2001 - believes the Newcastle-born midfielder is being underused by the national team.
Carrick gave United the lead just seven minutes into their clash with the Turkish champions with a fine strike, and soon after ex-Liverpool and Manchester City star Hamann took to Twitter to express his admiration for the West Ham academy graduate.
He tweeted: "Great goal by Carrick, how he doesn't start for England I will never know.
"He [Carrick] is the best holding midfielder England got by a country mile."