As much as he enjoyed playing at Murrayfield on Tuesday, and being part of the team that knocked KR Reykjavik out of the competition, the striker knows Champions League nights on their own patch will be even better.
Griffiths and his team-mates last night found out who stands between them and realising this dream as Legia Warsaw defeated St Pat's to book their place against Ronny Deila's side in next week's third qualifying round.
The first leg of that will be played in Warsaw on Wednesday, with the return again being staged at Murrayfield on Wednesday, August 6 as Celtic Park will still be in the process of being converted back to a football stadium after hosting the Opening Ceremony of the Commonwealth Games.
It will be the venue for the play-offs, however, the first round at which the famous Champions League theme music is played.
And it's on that Griffiths now has his sights set. It will be the first chance to take part in a big European game there for the man who joined the club in January from Wolves.
Griffiths said: "When the teams walk out and you hear the Champions League music and the fans go mad, it makes the hair on the back of your neck stand up.
"That's where you want to be. One of the big reasons I joined Celtic was I knew I would get the chance to play in Europe.
"And there's no bigger stage to play on than the Champions League."
He has sampled such nights as a fan. Now he wants to take centre stage - and the bigger the opposition, the happier he will be.
"I've been to a couple of Champions League nights, and I've never seen an atmosphere like it," he said,
"Hopefully, I can relive those special nights at Celtic Park."
Reaching the Group Stage would afford even more chances to enjoy such nights, though, for a change, he'd hope to see a Celtic win.
Griffiths explained: "I was there against Barcelona, when they beat Celtic 2-1 (2013), and I was at the Manchester United game when we drew 1-1 (2008)."
For now, though, Griffiths is focusing on ensuring he is part of Deila's team for these vital qualifying games.
And that means adjusting to what the new boss wants.
The Scotland striker has been operating on the right in the first two competitive games of the campaign and told the Celtic View: "The manager has stressed he doesn't want to play me just as a striker.
"He also wants me to play out wide, which I am happy to do - so long as I am in the team.
"The one part of my game I need to work on is my defensive side.
"But going forward shouldn't be a problem. It's been a new learning curve for me."
Ironically, while the man known for his goals has been concentrating on defending, central defender Virgil van Dijk has already popped up with two goals this season.
His double got the Hoops off and running on Tuesday and brought huge praise from his partner at the heart of the Hoops rearguard, Efe Ambrose.
The Nigerian said: "First of all, I'm happy we're through to the next round of qualifiers, but I'm particularly pleased with a second consecutive clean sheet from our first two competitive games.
"I can play with Virgil with my eyes closed. But seeing him score a brace is surprising.
"I'm glad he scored and he is every central defender's dream partner."