The Reds began the campaign with Champions League aspirations but have struggled to live up to expectations in the Barclays Premier League, particularly during 2012.
Kenny Dalglish's men have lost 10 of their 17 league games since the turn of the year, winning just four.
Yet amid that dismal sequence, the Merseysiders have managed to win the Carling Cup and secure a Wembley return in tomorrow's [Saturday] FA Cup final against Chelsea.
Because of that, Molby believes history yet could look favourably on a trying season, although he concedes there are mixed feelings on the matter.
The Dane, speaking at the BBC's Euro 2012 launch, said: "I don't know whether winning a trophy can make it a bad season, but winning two trophies would make it a great season, for sure.
"Having said that, there have still been a lot of disappointing results and performances in the Premier League that have been very difficult to forget."
Renowned for his passing ability, Molby played for the Anfield club throughout Dalglish's highly successful first spell as manager.
The Reds won three league titles and two FA Cups during Dalglish's stint in charge from 1986-91 and Molby is convinced the Scot is the right man for the job now despite criticism.
Dalglish has been knocked for the quality of his signings since returning to the post last year as well as being castigated over his handling of the controversial Luis Suarez affair.
Molby, who made 292 Liverpool appearances from 1984-96, said: "It is a project - you have got to give Kenny some time.
"If you think he is the right man you have to give him time.
"The big thing is the summer - is there going to be money available?
"What appetite do the owners have to go again? It is going to be really interesting.
"I'd back Kenny. I played under Kenny and have no complaints. He did a super job when I was there.
"I understand football has moved on but I still think he is the right man."