Former Chelsea centre-back Ivanović wasted little time in wiping out Celtic's first-leg 1-0 lead, powering home a header in the eighth minute to mark his 34th birthday with his third goal in the competition this season.
After a 1-0 win in last week's first leg at Celtic Park, the Hoops will have been hoping to carry on their European adventure and reach the last 16 of a UEFA competition for the first time since facing Juventus in the Champions League five years ago. We didn't close the space quick enough.
"There is still an bad lot of work for us to do but, when I take a step back, there have been a lot of positives for us in Europe this season." said Rodgers.
"Of course, we would have liked to have had one or two more goals but the concentration and our quality in our game was at a very high level".
Branislav Ivanović had a goal and an assist to help Zenit Saint Petersburg beat Celtic, while RB Leipzig beat Napoli on aggregate despite losing their second-leg match. We're too deep and have to press the guy who was shooting.
Celtic vs Zenit St Petersburg LIVE STREAM: How to watch Europa League clash online
But, at 2-0 down, we were still in the game and we had to show bravery.
"There's still an bad lot of work for us to do, but taking a step back, there have been a lot of positives for us in both European competitions".
"For us, we have analysed the game from the first leg and, even though we played very well, creating opportunities and didn't concede, there are still areas where we can be better".
"We were one step away from the miracle", said Napoli's Brazilian midfielder Allan.
The stadium's roof was closed over which was good news for the players and 50,492 supporters, including several hundred in green and white, in light of the sub-zero temperatures outside. Celtic are a strong team but we played very, very well.
"But frankly, after a 3-2 defeat on home turf, we were in a hard position".More news: Moscow sends new SU-57 stealth jets to Syria
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