The 28-year-old had taken time away from football seven months ago due to depression.
“Words can’t describe how good a feeling that was when the ball hit the back of the net,” Griffiths said.
“My kids were watching back home, I had friends in the stand. I was close to crying, I’m not going to lie. But I just had to refocus and see the half out.”
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The match was his second since returning to first-team training, having come off the bench in last week’s win over FK Sarajevo in the previous round of qualifiers.
The goal, a curling left-foot effort from around 25 yards, and Celtic’s third of the night, was his first since 24 November.
It drew comparisons with the two stunning dead-ball efforts Griffiths struck in Scotland’s dramatic 2-2 draw with England at Hampden during World Cup qualifying two years ago.
“It’s up there with the England moments, if I’m honest,” the striker added.
“A big thank you to my team-mates and everyone connected with the club – if it wasn’t for them then I wouldn’t be back on the pitch.
“Hopefully that’s the start of more goals. My kids were watching me and I had friends in the stands too. I was close to crying.”
Celtic boss Neil Lennon says the ovation of the Parkhead crowd “should mean to the world” to Griffiths.
“You always think he’ll hit the target or make the goalkeeper make a save,” Lennon told BBC Scotland. “It’s a great skill he has, he’s a natural-born goalscorer.
“There is an amount of anticipation and to be fair the reception he’s got from the players, the supporters, the club, that makes me very proud. It’ll do his confidence the world of good.”