Portugal international Danny's goal was enough to eliminate the Primeira Liga champions from Group C in an otherwise turgid game at the Stadion Petrovsky, with Luisao's late dismissal another rare moment of drama.
Jesus especially pointed to a first-half chance for Eduardo Salvio, who nipped in ahead of Domenico Criscito in the penalty area, but could not beat Yuri Lodygin when one-on-one.
"It was a tough game for both teams," he said. "We conceded a goal in our best period.
"In the first half hour we were not so well, we struggled to adapt to the weather, but the best opportunity was ours - through Salvio.
"In the second half we reacted very well, with great ball movement like I expect.
"We could have scored through [Nico] Gaitan and Luisao, but it was Zenit scoring.
"We did not deserve it but we come away from here with defeat and we are out of the Champions League."
Salvio was keen to remain positive despite elimination, but hailed the brutal nature of European football's premier club competition after Benfica dropped out at the group stage for a fourth time in five seasons.
He explained: "Our goal was to progress through this competition.
"We must continue to work hard if things are to go our way.
"We must raise our heads and look to the future.
"The Champions League is like this, if you fail to score you can suffer at any time."
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