The Blues had come from 2-1 down at the break to lead 3-2 going into stoppage time, only for a fine Magomed Ozdoev strike to deny them victory, meaning that Juventus leapfrogged the Blues into top spot after they beat Malmo 1-0 in Turin.
Two goals from Timo Werner and Romelu Lukaku's first since returning from injury looked to be enough for Chelsea before Ozdoev equalised in the 94th minute in the Gazprom Arena.
Tuchel's side was forced to settle for second place in Group H, and the German was particularly annoyed to concede three goals in a game for the second time in a week, having seen Chelsea lose 3-2 at West Ham on Sunday (AEDT), which also cost it top spot in the Premier League.
"If you are coach of Chelsea and you concede six goals in two matches, four times we've given the lead away, my ambition to talk about individual performances is not so high," he told reporters after the game. "We can't be happy today or against West Ham.
"It is like that now not to talk about individual performances. Nobody can be happy.
Chelsea started brightly, taking the lead in just the second minute through Werner, but were put under plenty of Zenit pressure for most of the first half, with the hosts scoring twice from nine shots they were allowed in the opening 45 minutes, before a back and forth second half.
"I think we had a very good first 15 minutes but we stopped doing the things we did," Tuchel added. "I had the feeling, and this is my opinion, that we forgot why we were the better team. And once this drops, once we start managing results, we get punished.
"It happened against West Ham and today. The reaction is good because it shows that it's not about what we can do. When we concede goals we can show a reaction but once we have the lead, we give it away again.
"We start playing balls back, not attacking with the same aggression and hunger than before. We got punished twice and it is for me the level of investment we have to do right no matter what is on the scoresheet."
When asked whether a deeper look was required having seen his team give up leads against both West Ham and Zenit, Tuchel said: "My analysis is very clear: our behaviour changes when we have a lead and this is something we've never done and should never do.
"The challenge is to close the door and minimise the possibility. We need a higher level of sprints, runs, concentration levels. The basics need to be pushed while we are in the lead. They can't drop when we are in the lead. It's not the big picture."