Tuchel was scathing of his side who have left themselves with a mountain to climb in the second leg in Madrid, with Karim Benzema netting a hat-trick.
Benzema put Real ahead two goals up with strikes in the 21st and 24th minutes, before Kai Havertz pulled one back before half-time.
The France international swooped on an inexplicable error from Edouard Mendy early in the second half to add a third.
“It is a heavy loss,” Tuchel told BT Sport. “It was one of the worst first halves that I saw from us here at Stamford Bridge.
“Individually and as a team it was by far not enough. It was far from our standards and then you lose games. We had 16 shots in the second half. You can always come back and win it but when you kill the game by yourself after 45 minutes it is harder and harder.
“If we keep playing like this we will lose at Southampton and then we will get hammered at the Bernabeu.”
Elsewhere, Villarreal claimed a 1-0 home win over German champions Bayern Munich with Arnaut Groeneveld’s eighth-minute goal.
Bayern boss Julian Nagelsmann said: “We deserved to lose. We weren’t good today. In the first half, we lacked power in defence and had too few chances.
“The second half was a completely wild game. We gave up control because we were desperate to score, but we could have conceded two more.”