Kris Commons opened the scoring with his 20th goal of the season in the eighth minute but the England international kept Hibs at bay with several good saves - the best from Sam Stanton in the second half when he pushed away a goalbound drive - as Terry Butcher's men fought their way back into the match.
However, a brilliant free-kick from Dutch defender Virgil van Dijk deflated the home side before substitute Teemu Pukki, on at the interval for Nir Biton, added a third with time for Commons to slam in number four from the spot after Hibs defender Alan Maybury had fouled Pukki.
The Hoops boss, however, was keen to point out why his side have not lost a league goal in nine games.
"We were worthy winners," said Lennon.
"I think the scoreline probably flattered us a bit but you have to take your hat off to the goalkeeper.
"He made one unbelievable save. There are not many keepers who can make those kinds of saves and thankfully he is one of them.
"It looked a goal all the way and how he got his hand to it and pushed it away, I don't know.
"It showed his concentration level, when he is not doing a lot, he can switch on and be the barrier he is at the minute.
"We got better as the second half wore on and obviously the second and third goals were magnificent in their own way.
"Two goalkeepers wouldn't have saved Virgil's free-kick, the execution was world class."
Lennon does "not know anything" about reports linking him with Falkirk's 19-year-old defender Stephen Kingsley but is confident that Forster will still be at Parkhead when the transfer window closes on Friday.
The former Celtic skipper said: "It wouldn't surprise me if an offer was to come in but we are not encouraging it.
"I think he is really happy here. I know he has personal aims for the future but the short-term future is with Celtic."
Stanton, making his first start for Hibs, was ready to acclaim a goal before he saw Forster fly across to claw his shot away.
The 19-year-old said: "I was almost away celebrating. I couldn't believe I had hit it so well but it was a brilliant save."
Butcher was pleased with his side's efforts, saying: "We didn't deserve to lose 4-0.
"It was a quick debrief to the players and I told them they could hold their heads high - particularly after the second half."
However, the Englishman was unhappy with referee Craig Thomson's "bizarre" decision to penalise defender Michael Nelson for the handball which led to Van Dijk's free-kick goal, but will not take it up with the Scottish Football Associations's head of referee development John Fleming.
He said: "The same referee didn't give a handball against the same player for the same incident at Aberdeen. And then we have a handball by a St Mirren player at the game last week which is not given.
"The ref said he cautioned Michael because he stopped the ball going through to an opponent.
"But if you look at the Aberdeen game with the same referee, same player, same incident he doesn't give a free-kick or a penalty.
"Last week Willie Collum - when the St Mirren player handles the ball not once but twice - he gives nothing, yet today's referee would say that should be a penalty.
"I don't know what the rules are and how the refs interpret that. I don't want to speak to Craig Thomson about this.
"If I really say what I think about the referee's performance then I would be in trouble with Mr Lunny (Vincent Lunny, SFA's compliance officer) so I'm not going to go there.
"It's a waste of time calling John Fleming. A waste of time."