His pledge comes after Sir Alex Ferguson suggested that it is now a two horse race between United and City for top spot.
With the Club World Cup in Japan looming, the Blues could be 19 points behind Fergie's side by the time they play Aston Villa two days before Christmas. Benitez, though, believes Chelsea have what it takes to come from behind and take the title.
"I don't know what he has said and I'm not thinking about it. I'm only thinking of my team," he told The Mirror.
"But I'm not worried about the distance. It's important we win so we are close, but all we can do is think about one game at a time.
"We have to improve the team and be mentally strong enough to compete in the second part of the league.
"If we can be closer sooner rather than later, much better. Obviously we'll have our chances if we start winning games."
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"At Valencia, we were eight points behind in February," he recalled. "If we have to do the same here, we will do it.
"But we have to show the same character. The main thing is about the evolution of our team. If we're stronger, we'll be able to win games in a row. We have to find form."