The Northern Ireland forward was emotionally pictured with his head in his hands following his team’s defeat to Slovakia in the Euro 2020 play-off final at Windsor Park.
Lafferty played while mourning the death of sister Sonia earlier this month, and just days after the 41-year-old’s funeral wore a pre-match t-shirt tribute showing the pair.
Afterwards the striker, now playing in Italy, broke down on the pitch at full-time and a photo posted on Twitter was liked by Griffiths’ @Leighgriff09 account which has since been closed.
Switching social media platform, Griffiths posted his explanation and issued an apology on Instagram.
He wrote: "Not that I should have to, but after what I'm seeing on social media I feel I need to.
"I want to state that I was not slagging Kyle Lafferty for losing a family member, that is the lowest of the low and not the type of person I am. The picture was in a Northern Ireland strip and the fact they didn't qualify and we did, which has been a huge achievement for the entire nation.
"Everyone gets carried away and people think I liked it because his sister died, absolutely not.
"We won, they didn't, we've been mocked for years about failure, but we did it.
"I want to apologise unreservedly for any misunderstanding there has been towards Kyle and his family."
Griffiths was an extra-time substitute for Scotland in the dramatic play-off win over Serbia and struck the first penalty in the shoot-out.