The Scottish champions had won the first leg 5-0 but suffered a 4-3 defeat in Kazakhstan, where they scored through Scott Sinclair, Olivier Ntcham and Leigh Griffiths.
Rodgers told BT Sport 2: “It’s mixed emotions because we didn’t defend well enough and our possession at times wasn’t good enough either.
“I said to the players (at half-time) we started the game very well. We wanted to control the tempo but we were too loose in our passing and our positioning, we weren’t compact enough when they had the ball. That didn’t allow us to press.
“I thought we were going to get through this campaign without the anxiety but that little period (at the start of the second half) they scored two quick goals. We were working on the side to plug gaps.
“I then have to give credit to the players because they were on the ropes for 15-20 minutes, but they regained their composure.”