Rodgers admitted it was "very difficult" to get his head around his side's defending which left them in a Europa League play-off spot where they will play Latvian side Spartaks Jurmala or Lithuanian side Suduva.
A 2-1 defeat in Greece ensured Scottish Champions would not compete in the top tier of European football this season.
"I thought a lot of our build-up play was worth something from the game but you can't defend that softly", Celtic manager Rodgers told BT Sport.
"When you add that to the goal we conceded in the first leg then we're really disappointed".
Death toll in Genoa bridge collapse rises to 35
He told RAI television the government meant to cancel its deal to manage the A10 toll motorway connecting Genoa to French border. Authorities are also advising residents to avoid the highways and to just use local roads for their daily activities.
The 27-year-old is refusing to discuss a new deal and The Sun claims he declared himself injured at Lennoxtown on Friday- 24 hours before Celtic's 1-0 defeat away to Hearts.
Losing Boyata would be a significant blow to the Celtic after his significant improvement under Brendan Rodgers at Parkhead.
Asked if he felt frustrated on a night where defensive inadequacies proved costly, the Northern Irishman said: "Yes, of course. We have to find a way to get a result".
He spoke to the Belgian website DH.be and said following on the issue: "When I hear I've refused to play since I came back from vacation, it's wrong".
"But he wasn't here and we look at the performance without him and I can't think any more than that".