City are six points behind the Gunners and can cut their Prem lead by beating Fulham on Wednesday.
Guardiola said: “All we can now do is breathe down the neck of Arsenal and be there. If they sleep, if they make a mistake, then we have to use it.
“It’s a big gap but many things can still happen. It’s 13 games in the Premier League — from my little bit of experience that is a lot of time, a lot. It’s proper.”
Guardiola added: “We’ve won – we finally won at Anfield.
“We just need victories like this as we have many good things to fight for – the title, Champions League and Carabao Cup.
“Maybe we still are not totally ready.
“Maybe in one month we will be ready because we’ll have some players back.
“This is an incredibly tough place to come, so I’m really proud.”