The reigning Scottish champions flexed their muscle with a 4-0 victory at Tynecastle and Forster feels it was important to bounce back swiftly from the weekend's shock loss to Inverness for which Lennon copped plenty of flak from the Hoops faithful.
"The gaffer had asked for a reaction from us and that is what he got," said Forster.
"There were harsh words after the weekend. You can't get beat at home and drop the number of points we have at home and be happy about it.
"We're obviously disappointed with our home form and it's important now that we put a run of wins together and show the consistency that we did last season.
"We know we can play like that, but now it's doing it consistently and that's the challenge for us in the league, to keep up that level of performance.
"It's also about grinding out wins if we have to.
"We were a bit stunned by the manager threatening to quit.
"He has done a fantastic job since he came through the door and we players are responsible for what goes on on the pitch."
He added: "If you lose then you've always got your critics. But it's important that we go out and don't worry about what people are saying.
"We need to show what we can do and we've got our own pride to show. "It's important that we focus on that and play the best we can for everyone."