The Reds are currently 14th in the Premier League, just three points off the bottom.
However, Gerrard thinks that after picking up their first win against Norwich City, Liverpool can kick on and move up the table.
When asked what Liverpool's ambitions were this season, the 32-year-old replied: "Top four and a trophy.
"The Norwich win will be a catalyst to push us on. We should have a few more points but teams will find it difficult against us.
"I'm confident we can go on a run of winning games. They are good opportunities but also tough games. They are games we should be winning though, especially at home.
"We have been playing well for a few weeks so if we keep it up, I'm sure we can win the upcoming games."
Liverpool's next match is against Stoke City on Sunday afternoon.