Griffiths took his tally to four goals in three matches since his recent arrival from Wolves, a move that was apparently not entirely popular among some Celtic supporters.
Lennon said: "His movement was giving Inverness trouble. His first goal pleased me the most, we have been crying out for a penalty-box striker and that was a great ball and a great finish."
Celtic have been looking for a striker to replicate Gary Hooper's goal return, after the Englishman joined Norwich last summer, and Griffiths is hopeful he can deliver.
"When the fans heard there was interest in me they didn't want me here but as long as I have the manager's backing that's good enough for me," Griffiths said.
"But I am trying to prove everybody wrong and trying to score as many goals as I can and the first one was probably my best.
"I sclaffed it in but that the kind of goals I like to score. People normally associate me with long-range shots and trying to beat people but front post, that is where I want to be.
"That is what the manager wants. He wants a penalty box striker. He said that Gary Hooper was one of the ones to emulate and if I was half as good as he was then he will be happy. "
Caley Thistle boss John Hughes tried to take positives out of the defeat as he prepares team for the Scottish Cup quarter-final with Dundee United and the League Cup final against Aberdeen.
Hughes said: "We can take a lot from the game. One thing I will say is that we came and had a go. But Celtic are the best in Scotland and you need to learn from these games even in defeat.
"I don't think we'll ever get to where Celtic are and I said that to our boys after the game. But that's not our fight. It's the rest of the games. It won't harm us.
"The next month will define our season. We have Dundee United next week in a quarter-final and then a Scottish League Cup final to look forward to."