Sir Alex Ferguson's side edged one ahead of their arch-rivals in terms of championship titles with their 19th success in May.
By contrast, Liverpool have not won the league since 1990 - when Kenny Dalglish was in charge first time around - and their last trophy of any kind was the 2006 FA Cup.
With owners Fenway Sports Group willing to invest heavily in players for the long-term future - having recently signed England Under-21 midfielder Jordan Henderson in a £20million deal - Gerrard is optimistic they can match United and he will 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 programme of rehabilitation - the club's physios have been working with him every day at his holiday home in Portugal - after groin surgery in March but he will be ready for the start of pre-season.
It is has been the longest spell on the sidelines of his career but the England midfielder is confident he and Liverpool will feel the benefit when the new campaign kicks off in August.
"I want to come back with a bang, I want to have a big season," Gerrard told liverpoolfc.tv.
"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.
"I've had a rest mentally, my injury's coming on well and I can't wait for the season to start.
"There's still a lot of time for me to achieve bigger and better things. I'd like to finish my career with a few more trophies.
"I always look at the 35 marker. If I get there and I'm still involved with Liverpool I'll be delighted but at the moment I'm feeling as good as ever.
"I've had time to get my body right, get my body strong. I'm still four or five weeks away from playing a game but I believe I'll come back in better physical condition than I've ever been."