The Spain midfielder believes that the champions' first half display at St James' Park was one of their best of the season as they recovered from their dramatic derby defeat.
The Spaniard identified Roberto Mancini's team's first half display as one of its strongest of the season as it raced into a 2-0 lead.
And the former Benfica star, who scored City's second goal, thinks that the club can hunt down league leaders Manchester United if it can replicate that type of performance on a regular basis.
He added, "If we play as well as that then we are going to be very difficult to stop. If we continue to have that attitude, we will be very hard to beat.
"The good thing about the Premier League is that anyone can pull off a surprise and there are other teams who can push up the league and challenge for the title. But if we finish above United, I think we will win the league."
Garcia was delighted to see City bounce back so quickly in the wake of its dramatic 3-2 derby defeat against United the previous weekend.
The 25-year-old stressed the importance of immediately returning to winning ways and insists the City players have continued to believe in themselves.
"It's normal to be feeling down after a result like that [against United]," Garcia stated. "But we had to lift our heads up. We had to continue to believe in ourselves and remain positive, and I think we have shown that against Newcastle.
"It was an important game after what happened against United. We had to show we could continue to have a winning mentality."