The 32-year-old England international feels that the Merseyside giants, who won the last of their 18 English titles back in 1990, have fallen behind the leading lights in the top flight in recent years, a point illustrated by their eighth-place finish last season.
New manager Brendan Rodgers was brought in over the summer to replace Kenny Dalglish and finally picked up his first league win of the new season at the sixth time of asking with a 5-2 romp against Norwich.
With the club in a transitional phase, Gerrard believes that finishing in the top four this term amid the ever-increasing competition in the Premier League and securing a return to the Champions League should be their main target.
He told the Sunday Times: "There's not just (Manchester) United and Arsenal now but City, Chelsea and Tottenham. Newcastle coming as well. The Premier League has become a lot more difficult to win for everyone.
"We were eighth last year. If this season goes well, we get a bit of luck, improve, we have an outside, no, a 50-50 chance of being in the top four. That's being realistic. It's achievable.
"But even if we do sneak into the top four I'll be 33 at the end of the season, so that's why it'll be a miracle if we win the title before I finish.
"But I'll keep fighting. I'll keep trying and see what happens."
Gerrard has also revealed how an infection in a seemingly minor ankle injury last season threatened to bring his career to a premature conclusion, with emergency surgery required just two hours after he was eating a pre-match meal with the rest of the team prior to the clash with West Brom.
He said: "The doctor was unhappy with the colour and size and had sent the sample for tests. There was a severe infection.
"If I hadn't had the fluid out within 24 hours I wouldn't have had a cartilage. The bug would have eaten it. I'd probably have never played again, or even trained.
"In my mind, as the operation began, was, 'This could be the end'.
"I owe the doc and Chris Morgan, our physio. Last year put my career into perspective."
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