Liverpool are unbeaten through the opening 12 matches of the Premier League, but still don’t sit top of the table.
Reigning champions Manchester City are also unbeaten, as are Maurizio Sarri’s Chelsea.
Liverpool were tipped to be the closest challengers to Pep Guardiola’s side this season, but have struggled to find their best form despite the unbeaten start.
The Anfield outfit have never won the title in the Premier League era, with their last trophy coming in the League Cup in 2012.
And Fowler believes Klopp needs a trophy for this season to be successful though admits City provide the biggest block in that quest.
“A gauge is getting as high up in the league as they can,” Fowler told Sky Sports’ The Debate.
“As much as we talk about Liverpool being this unbelievable side who are easy on the eye and great to watch, there comes a time when you need to start winning stuff.
“I think Jurgen Klopp’s getting together a great, great squad but I think one of the problems we have is Manchester City are brilliant.
“That’s one of the big problems. You can get a wonderful side put together but you’ve got to try and catch them and then hang onto their coat tails.
“For me, no [finishing in the top four isn’t enough].
“It really isn’t because I’m not one of these fans that think you should be celebrating finishing fourth.
“I think a chairman or the owners should be the ones celebrating. For me that’s celebrating mediocrity. I’ve always wanted to win stuff.
“I wanted to be remembered for what trophies I won as opposed to where I finished in the league.
“I understand why clubs are happy finishing in the top four but I think a club the size of Liverpool’s stature should be finishing in the top four all the time anyway.
“As I said before, there comes a time when you need to win a trophy. I don’t care if it’s a League Cup. People will belittle that but I’ve won one, it’s a brilliant trophy.
“When you think of football in terms of what you can win there’s an FA Cup, a League Cup, the Premier League and the Champions League. There are only four trophies so it’s tough.”