The Reds finished second in 2008-09 with a points total of 86 that would have won the league in several other seasons, but they have never come as close in Gerrard's tenure as skipper.
With the Manchester clubs and Chelsea all strengthening in the summer, the 32-year-old realizes his hopes of bringing the title to Merseyside are unlikely to happen, especially with other up-and-coming rivals also hungry for success.
"It will be a miracle if I now realize my dream of winning the title with Liverpool," Gerrard said in his recently published autobiography My Liverpool Story. "I say that because of my age and where we finished in the league the past couple of years. And also the situation we're in with the rivalries.
"There's not just 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."
Despite Liverpool's fine 5-2 win at Norwich on Saturday, the club's poor early-season form has already led to an 11-point gap between the Reds and league leaders Chelsea, which may prove to be too large a deficit for Brendan Rodgers' side to overcome.
Even so, Gerrard claims that, with improvements, the club will be capable of challenging for a UEFA Champions League qualifying position by the end of the season.
"We were eighth last year. If this season goes well, we get a bit of luck and improve, we have an outside, no, a 50-50 chance of being in the top four. That's being realistic. It's achievable," Gerrad said.
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