Celtic have "lots to work on" after the 1-1 draw with Kilmarnock, says manager Neil Lennon, who refused to blame defender Christopher Jullien for the Scottish champions' slip-up.

Jullien's clumsy shirt tug on Nicke Kabamba allowed Chris Burke to level with a first-half penalty.

Celtic had led through Ryan Christie's speculative free-kick, but struggled to create clear openings.

"Chris is always a slow burner to get going," said Lennon.

"He was the same this time last year. There's a bit of rust there, but he will get better as the season goes on.

"He is disappointed but that is not the reason we dropped two points. We weren't good enough in the final third with all the play we had.

"I'm frustrated. We got off to a good start and gave away a poor goal. We dominated the second half and didn't find the answer."

Lennon confirmed Celtic are conducting an investigation after injured striker Leigh Griffiths was reportedly warned over his conduct after holding a gathering at his house which appeared to breach social distancing guidelines.

"I am not convinced it is a big issue and hopefully it will be resolved in the next couple of days," the Celtic boss added.