Youri Tieleman’s speculative 25-yard strike settled matters in front of 21,000 fans as Leicester won their first FA Cup final at the fifth attempt.
Chelsea have now lost back-to-back FA Cup finals after last season’s showpiece defeat to Arsenal under Frank Lampard.
The Blues were denied a late equaliser against the Foxes by VAR as Ben Chilwell was adjudged to have strayed offside in the build-up to Wes Morgan’s own-goal.
Tuchel admits his men did their best to win the game but luck eluded them on the day.
"Of course we're disappointed, but we're not angry with our performance or our boys," Tuchel said at a post-match news conference.
"I think this performance is enough to win the game. We were simply unlucky.
"We've never hidden the fact that you need luck in this game to win at this level. In some moments you need little details, some decisions, referee's decision-making, sometimes a shot like today.
"I think we defended very, very well. We were very aggressive in counter-pressing, we defended very high up the pitch. We did not allow any counter chances for one of the most dangerous counter-attacking teams in Europe.
"We did not allow any half-chances, any chances. I was absolutely happy with the work rate and intensity."
Chelsea still have a chance to end the season with a trophy as they face Manchester City in the UEFA Champions League final on May 29.
