Having taken the lead through Kai Havertz in the 33rd minute, the Premier League leaders had numerous opportunities to double their advantage and end the game as a contest.
However, after Burnley mustered a rare attack and equalised through Matej Vydra, the Blues were unable to find a winner during the final stages.
Despite the result, Tuchel was quick to praise his side, claiming that Burnley had found a way to 'steal a point' at Stamford Bridge.
Tuchel is quoted by BBC Sport as saying: "It was a fantastic 90 minutes when you look at performance. It can only happen in football. That's why everyone loves the game – a team can steal a point if the other team forgets to score the goals they deserve.
"Of course I'm disappointed. If we played this game 100 times, we'd win 99 times. Today we didn't win it. The second goal would have decided it. It's always possible you miss one ball, one cross, and this can happen.
"It's our fault. We should have scored. We created so many chances. You have the opponent where you want to have them. You create so many chances. We let them believe it was possible to steal a point by pure luck and that's what happened.
"This is not the first game like this and won't be the last. I was impressed by the performance, the attitude, the quality. It's football, it was against us today. You know this can happen. In real life these things happen. We are in a good place. We deserved more today. On another game we maybe get lucky and steal some points."
Chelsea now sit just three points clear of Manchester City, while Liverpool can move to within a point of the Blues with victory at West Ham United on Sunday afternoon. body check tags ::