In the end, Hulk's away goal was enough to see Zenit progress to the next round of the Europa League.
"It was absolutely breathtaking," said Rodgers. "One of the real values of this football club is unity. Everyone came together tonight and we just missed out.
"Hopefully in the future there will be many more great nights for us to celebrate.
"Having sampled that as a manager in the home dugout, I want many more occasions like that with bigger prizes.
"We really needed them tonight and they were right behind us all the way. We're disappointed we couldn't do it for them, but hopefully there will be many more in the future that we can do for them."