Sir Alex Ferguson’s side recorded their 19th Premier League title last season, edging one ahead in the long-running battle between the old foes.
With Liverpool owners willing to spend big after the aqcustion of Andy Carroll and Luis Suarez last season and having recently signed England Under-21 midfielder Jordan Henderson in a £20million deal, Gerrard is confident the Anfield side can match United and suggested he wants to win more trophies before the end of his Anfield career.
"As a Liverpool fan and a player it's frustrating when you see your arch-rivals lifting trophies but you've got to give credit where it's due. They've won it, they've overtaken us," said the 31-year-old.
"Now the challenge for us is to equalise. We've got to make sure we've got a squad capable of going into the season and competing with Manchester United.
"It's a big statement by the club getting a big signing in early and now we're watching anxiously for a few more to follow. It's exciting times.
"It's important this team delivers very soon because we've been a number of seasons without putting a trophy in the cabinet and that's not what Liverpool is about.
"I want to play well, I want to score goals - but it's much more important that the team plays well and we all end the season happy."
Gerrard is currently undergoing a rehabilitation programme after missing the end of last season after undergoing groin surgery in March.
"I want to come back with a bang, I want to have a big season," Gerrard told Liverpool's official website.
"It's been non-stop football for me since I started when I was 17. I've never had a period of more than four or five weeks out of the game, so it's been nice to rest mentally.
"You don't want to miss games but when you're watching them it gives you that edge, that buzz to get back.
"I'll come back hungry and hopefully there's a very productive season ahead for me."
