The European champions dominated proceedings, with 25-5 shots along with 70 per cent possession as Kai Havertz gave them a 33rd-minute lead.
But Burnley found a way back in the 79th minute when Matej Vydra tapped in from close range as Jay Rodriguez broke the offside trap to lay off the decisive pass.
“Burnley were very lucky to draw but that’s football,” Tuchel told reporters. “We were very lucky to escape with a clean sheet at Brentford. That’s why everybody loves the game.
“I stick with my feeling from the sideline and I have proof from all data that we did a fantastic match. I liked to be attitude. I liked the intensity. I liked the concentration level. These are what you need after seven wins in a row.
“It can happen in football that sometimes, unfortunately like today, somebody else steals some points.”
Chelsea remain top, holding a three-point lead over Manchester City, while third-placed Liverpool are a point further back but play West Ham United on Sunday.
Manchester City comfortably accounted for rivals Manchester United 2-0 after an early Eric Bailly own goal followed by Bernardo Silva’s close-range finish.
City were clearly the better side, with 68 per cent possession at Old Trafford, along with 16-5 shots and 5-1 on target.
The best way to silence Old Trafford is to have the ballhave the ball and we did it,” City boss Pep Guardiola said.
Meanwhile, under-pressure United boss Ole Gunnar Solskjaer said: “We started the game off badly, passive. Its hard to talk at the moment.
“We play against a good team, dont forget that, but we were nowhere near what our standards and levels can be and thats something we have to get back to.”
Bottom club Norwich City won 2-1 at Brentford, their maiden victory of the campaign, although it wasn’t enough to save manager Daniel Farke’s job as he was dismissed post-game.
Brighton drew 1-1 at home with winless Newcastle, while Crystal Palace beat Wolverhampton 2-0 with Chelsea loanee Conor Gallagher scoring again.