Sturridge hit out at criticism and told people his future remained at Liverpool, which pleased Molby.
Sturridge dismissed any speculation surrounding his future saying he was happy at Anfield and hit back at critics questioning his desire to play after a retched time with injuries.
Molby wrote in his Liverpool Echo column: "Fair play to him for his media work before the Augsburg game. Liverpool fans still regard the club as big as any other and Sturridge looked at the situation and probably wondered why anyone would doubt that he wants to be here,
"It's been frustrating with the injuries and rumours but, believe me, every footballer wants to play football. It doesn't matter what the fans say, if you're a footballer, you want to be on that pitch.
"I think what he said when sat alongside Klopp was a clear statement that intends to hang around. Good.
"Fingers crossed he can stay injury free, because when he's fit and firing, everyone knows what Liverpool have on their hands: one of the best strikers in the Premier League."
Sturridge certainly came out fighting in Wednesday's press conference and seems determined to find some form in order to help the Reds a strong finish to the season.
He has appeared in each of the last four games for the Reds and looks set to start the League Cup final against Manchester City on Sunday, which is something that Liverpool will welcome as they have struggled in front of goals in a lot of games this season.
No doubt those critics will be silent if Sturridge manages to stay fit for a sustained run in the side and starts finding the net on a regular basis.