Forrest's 55th minute effort - which helped the Premiership leaders secure a 3-1 win which restored their three-point lead over Rangers - means he has now scored in 13 consecutive seasons for the club in the Scottish top flight.
The 30-year-old has been limited to mostly substitute appearances this season after battling back from injury, but Postecoglou was delighted with his display at Almondvale and insists he knows the worth of the Scotland international.
“He has had a tough time but I see him every day, you guys don’t," the Celtic boss said.
"That is how I make my assessments and he has worked really hard in training. It is not easy when you don’t get a run of games but the quality he has has always been there.
"I have had to be patient for when I can throw him in because I know he can certainly help us. He is one of the more experienced ones and he can definitely help us. He is a winner, you know. We are going to need those types.
“I don’t know if he was lacking in confidence. It lacks a little bit of rhythm and that spark you need when you are an attacking player. He is an experienced guy and he knew what he had to do and he played his role very well. He and Jota really set the tone."