The Liverpool boss has brought in several new faces over the summer including striker Peter Crouch and midfielder Mo Sissoko as the Anfield club look to defend their Champions League crown and improve on last season's 5th place finish in the Premiershop.
Benitez's side finished some 37 points behind champions Chelsea season, which had many fans disgruntled as Liverpool struggled to defeat some of the smaller clubs in the league and the Spaniard said: "I don't know how much closer we can get, but I am confident we will not be so far behind.
"I think the title race could be more open this year with the top three plus ourselves and maybe another club all challenging."
Benitez added: "It's not going to be easy to close a 37-point gap in one season but we will be closer this time.
"Chelsea enjoyed one of the best-ever Premiership seasons last year but if we improve, and if Arsenal and Manchester United improve, then I'm sure we'll all be closer to them."
Liverpool open their Premiership at Middlesbrough next Saturday, however, they face a tough Champions League third qualifying round first leg away to CSKA Sofia on Wednesday as they look to qualify for the group stages of the premiere European competition.
He continued: "I know the history of our club and I understand what winning the Champions League meant to our fans. But I also know we must do much better in the Premiership because this is also important to the fans.
"There will be more expectation on us to do better in the league and we must live up to that.
"I still have things to prove to people in England. I came here to win trophies over five or even 10 years, not just to win the Champions League. Part of my dream is one day to win the Premiership.
"I am not saying we will win it this season because you can never say such things in football but I can promise the fans we will work even harder than we did last year and we will do better."
Liverpool only managed 17 victories in 38 league games last season. Benitez said: "I am confident we will win more games both at home and away because we have a better squad and a better team.
"Over the next nine months we'll be able to use different players for different games and that will help us."