The one-goal lead from the first leg was reversed before half an hour had been played in Russian Federation as defender Branislav Ivanovic put Zenit in front with a header and Daler Kuzyayev netted in the 27th minute to turn the tie in the hosts' favour.
"The first goal from a corner is one that can happen".
Tom Rogic replaced Eboue Kouassi for the start of the second half, the Australia midfielder sending a shot over the bar within a minute of the restart. "We didn't threaten at all, because we were too negative in our play".
"But, to really threaten, you have to ensure you defend better and the third goal was a very disappointing goal to concede".
Celtic manager Brendan Rodgers says that the club can take some positives from their European campaign, despite them only winning two of the eight matches they played after qualifying for the Champions League.
"In this one, if we had played with a bit more courage and belief, we maybe could have got a result".
Last season's semifinalists Lyon won 1-0 at Villarreal to go through 4-1 on aggregate, while Sporting Lisbon and Viktoria Plzeň also reached the last 16.
"There is still an terrible 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. We need to be more patient and have a better structure at home sometimes.
"There have been aspects that have pleased me and we have taken steps forward with a lot of young players". Last week was an outstanding performance which would allow you to think you had a great opportunity to go through but if you don't start with that aggressive mentality, then it's really hard. We now have to finish our domestic campaign as strongly as we can and create another piece of history on that front.
The Italian said: "We deserved to win". "We played a very good game".
Despite the defeat to Zenit, Celtic still have plenty to play for this season, and look on course for another treble. "Tonight we scored three goals, had other chances and for 75 minutes didn't concede any chances to Celtic".