The Bhoys striker takes responsibility for the Hamilton draw.
The former Wolves hitman had fired the Bhoys ahead from the spot on 35 minutes, before a straight red card for Dedryck Boyata threatened the visitors' route to victory.
Despite being a man down, Ronny Deila's side could, and maybe should, have doubled their advantage shortly after the hour mark when referee Craig Thomson awarded them another penalty, but Griffiths saw his effort saved by Michael McGovern this time around.
Seventeen minutes from the end, Eamonn Brophy managed to salvage a point for the hosts in superb fashion, and the Celtic hitman was left kicking himself over what he feels should go down as two points dropped.
“I take responsibility. I scored the first and was confident for the second but I’ve got to give credit to Michael. It was a great save and they’ve kicked on and got a point," Griffiths told Celtic's official website.
“I thought he was going to change his mind and go the same way as the first time, but that’s twice he’s saved a penalty from me. Hopefully I don’t face him again.
“It’s annoying but we’ve got to accept that and take it forward. We have to concentrate on what we do and we’re going to be concentrating on Dundee on Wednesday.”
Despite the two dropped points, Deila's side remain seven clear of Aberdeen in second, though the Dons could and should reduce that to four points when they host St Johnstone today.
The Glasgow giants host Dundee FC on March 2 as they chase a swift riposte from last night's disappointment.