The Reds take on Roberto Mancini's side at Anfield on Sunday and the Scotland international knows how important it was to register a victory after their defeat at West Brom
Brendan Rodgers’ side fell to a disappointing 3-0 defeat at West Brom in their opening Premier League fixture, but bounced back with a hard-fought victory in Edinburgh on Thursday night.
Next they face the champions at Anfield, and Adam is sure their 1-0 win over the Jambos has given the Reds' players the confidence to beat Roberto Mancini’s side.
"I think that was the biggest thing [about the win]," he told Sky Sports. "We bounced back from losing the game at the weekend, which everyone was disappointed with.
"We knew it was going to be a difficult tie but we came through it, we won 1-0 and we look forward to Sunday now.
"The champions are coming to Anfield but they know they will be in as hard a game against us as we know we are going to have against them.
"Man City are a top team with top players but we have good players as well so we are looking forward to it, it will be a big match."
The 26-year-old continued to play down rumours over a possible exit from Merseyside, insisting he has no plans to move on.
"I still have three years left on my contract, I am happy here and I am looking forward to the rest of the season,” he added.
"This is a great club to be part of and a new era started under a new manager and I want to be part of it."