The Parkhead club had refused their ticket allocation for the first leg of the second qualifier in Belfast due to security fears.
However, there were around 300 Hoops fans in the Kop stand, set aside for them in a half-full stadium, to see attacker Scott Sinclair head the visitors ahead in the 17th minute before midfielder Tom Rogic made it 2-0 five minutes later.
A missile was aimed at Griffiths after he had set up the opener with a corner and - in the second half - he was booked by Spanish referee Alejandro Hernandez for presumably taking his time at a corner when objects came his way.
The Scotland striker was soon replaced by Moussa Dembele with Jonny Hayes replacing James Forrest to make his debut and he too had missiles launched at him when he took over corner-kick duties. There was more bad feeling at the end of the match when Griffiths came back on to tie a Hoops scarf to a goal post.
Asked about concerns over Griffiths when he was down in the corner close to the Linfield supporters, boss Rodgers, said: “I didn’t quite see what it actually was but if that is the case then of course there is always a worry.
“But I didn’t see or haven’t heard anything as of yet as to what was thrown on, I could only see it from the dug-out.
“It was maybe a bottle of some sort, but anything, whether it’s a coin or a bottle or whatever, shouldn’t happen.
“Players go on to the field and it should be a safe environment for them.
“You want the passion from the stands to stay in there. But if you take that away from it, it was a good evening.
“You sometimes get these scenes throughout the country, not just here but other places as well.
“Obviously it’s not what you wanted to see. The game was played in good spirit, in the main. So it’s not ideally what you would like to see. I thought it was strange him getting booked for it.
“But like I say the talk is more really on the football for us. The scoreline was okay, it could have been better but it gives us the advantage for the second leg.”
Linfield will most likely face a UEFA probe but manager David Healy, who thought his part-time side were “excellent considering the quality of opposition we were playing against”, claimed not to have seen any missiles thrown at Celtic players.
The former Rangers striker said: “I don’t think it was always going to happen.
“I think a lot of people in the media were making a big deal out of it.
“Linfield as a club have made giant strides over the years to try to cut that shouting and abuse out but you get that in Old Firm games, you get that in Manchester derbies, you are always going to get a ferocious red-hot atmosphere.
“Our fans back us - back the players and me - through thick and thin and hopefully they’ll continue to do that throughout the season.”