The midfielder believed his England colleague Gareth Barry would have been a suitable signing, however Barry's ¦pound;12million transfer to Manchester City means that will not be an option.
Gerrard said: "We are getting really close to becoming champions. Our next two or three signings as far as we are concerned are crucial to push on and try and go one better than this year. I am certainly not sitting here proud of not winning a trophy."
Gerrard insisted Liverpool should be looking for players "of Gareth's standard" if they missed out on Barry, and added: "He is English and you need English players at your club now."
Liverpool's captain is hurting at the club's failure to win a trophy during the 2008-09 campaign but believes a few more quality players could end the wait to take the Premier League title.
Speaking ahead of England's World Cup qualifier against Kazakhstan on Saturday, Gerrard reflected on Liverpool's battle with United for league glory, which the Red Devils won.
Gerrard said: "Has the season been a success or failure at club level? I think failure is a bit strong but you've got to be realistic and look at the big picture.
"We've finished the season without a trophy which hurts. But from a Liverpool point of view, a lot of progress has been made."
Gerrard would like more players of the quality of striker Fernando Torres to arrive at Liverpool. He said: "How do we go to the next step? Get more players of Torres' level. He is a massive player for us. You saw the impact he made in his first season and how good he has been when fit this year.
"If we can keep Torres fit, and had a little bit more quality to our squad, we can become champions. Manchester United won the league because they had that spark coming off the bench, that little bit more strength in depth."