The first leg of the second qualifying round tie was due to be played on July 12, at the height of the marching season in Northern Ireland, but it was then changed to July 14.
However, the Hoops decided that the potential for disorder was still too big a risk and ultimately opted not to take up their ticket allocation for the game in Belfast.
Northern Irishman Rodgers told BBC Sport: "That's the only sadness for me. It's a shame for Linfield and for Northern Ireland because football is a sport in this country that is loved and to have had the two sets of supporters there would have been fantastic.
"The Celtic supporters will travel worldwide but this is a game that the football club hasn't had the assurances for their safety, which is sad for me, coming back to a new Northern Ireland. Not being able to ensure that the supporters' safety is guarded, that's a problem for me.
"We will just focus on the football and next week in Glasgow there will be 60,000 there and we'll enjoy the football in the home leg as well. You always want to hear your own supporters, but it won't take a lot away from the actual game. It will be a good atmosphere, I'm sure."
The return leg of the tie takes place at Celtic Park on July 19.