The Reds have missed out on
Although Liverpool owners John W Henry and
"It has got to come," he said. "We are Liverpool. We can't finish eighth. We have got to put that right.
"I don't think it's ever happened that a team has gone from eighth to first but there are still other big targets for us to achieve short term.
"Getting in that top four again is certainly the priority. I am confident we will get it. If we can play like we did in a lot of games last season and take our chances, I think we will be high up in the table."
Gerrard, speaking on the club's pre-season tour of
He also admits there is pressure on the players to perform in the new campaign but has been impressed by the impact made so far by Rodgers.
"Kenny knows himself that when Liverpool finish eighth, the owners and supporters are going to ask questions," Gerrard added.
"While there was shock and disappointment at the time, you understood the decision. You move on with what the club wanted to do and they wanted
"I think we'll definitely see a much bolder Liverpool team. Over the years sometimes Liverpool have come up against certain type of opposition and we have shown them too much respect but I think this manager is the opposite and wants us to play like a big team.
"I've been really impressed with him."
Meanwhile, West Ham United has declined to comment on speculation linking it with a move for Liverpool striker
The newly-promoted Hammers are reported to have offered to take the Liverpool striker on loan for an initial fee of just over $3 million, with $24.1 million added on top of that to make the move permanent provided it avoids relegation from the English Premier League next season.
However, Liverpool is thought to be holding out for $30.1 million and would prefer not to loan out the forward, who cost the club $52.7 million from Newcastle 18 months ago.
Newcastle United had a loan bid for the 23-year-old rejected earlier this month while Fulham is also thought to be interested in ending Carroll's stay at Liverpool.
English Premier League
Andy Carroll is on the brink of joining West Ham United permanently after passing a medical with the Premier League club.