The Reds boss admitted the Uruguay international could have had a three before half-time, on one occasion rounding goalkeeper Alexander Kerzhakov but failing to find the net.
His misses, which also included a cheeky backheel from close range he put wide, kept Zenit in the game and with 20 minutes to go Hulk, from 30 yards, and Sergei Semak gave the hosts a significant lead in their last-32 tie.
"He could have had a hat-trick by half-time," Rodgers said. "It just wasn't his night but he's been brilliant for us all season. The important thing is that after his first one-on-one, he kept going and was still in there."
Costly defensive errors
Rodgers bemoaned the defensive errors which cost his side for the second time in four days after Monday's late slip-up at home to West Brom.
"Going into the last 20-25 minutes I was thinking we could win the game but we gave away two poor goals," he added. "The first one is a terrific strike but we are disappointed with the build-up and we could have defended it better.
"We ended up losing the game when we probably should have won the game. In six months, 12 months' time we won't be making those mistakes.
"This is a group that is growing and this is part of our growing pains. We have put in some terrific performances this season and not always got results but we have to be more clinical and that is something over the course of the coming months which will have to take place."
Liverpool face an uphill struggle at Anfield next Thursday to keep their European campaign alive but Rodgers is not giving up just yet.
"There is no way the tie is over, not by a long shot. We are more than capable of getting the goals back," he said. "I think the next goal is vitally important for us and what gives us hope is we created enough to win the game.
"If we get it early it can create the momentum for us. At 2-0 (down) you can retrieve something and it gives us a fighting chance."