Both sides hit the crossbar in the first half and both goalkeepers were forced into several decisive saves in an unrelenting game which ebbed and flowed.
The Blues extended their unbeaten Premier League run to 10 matches – 12 in all competitions – since Tuchel replaced Frank Lampard in January.
But the German said: "I think we could have won exactly the same game. We created enough chances, enough shots, enough touches to score one or two goals.
"Unfortunately and obviously we did not, so we have to live with a draw, but yes at the same time it was a difficult pitch, very difficult conditions, very slippery, very bouncy.
"But we accept all the difficulties in an away game against a team that puts a lot of pressure on you."
But Tuchel believed his side had held the ascendancy, adding: "We found many situations where we could escape the pressure, where we had high recoveries of the ball.
"But we were not clinical enough on the counter-attacks, our precision or the last touch."
Leeds fell one game short of setting a new club record of 19 successive league games without a draw, their previous one coming back in November – 0-0 against Arsenal.
Boss Marcelo Bielsa was clearly satisfied with his side's performance despite failing to score for a third straight match.
"Evidently we played against a team superior to ours," Bielsa said. "We did what was necessary to play a balanced game.
"At the end of the game, the chances of both teams were similar. It's true the superiority they showed in the first half was superior to what we showed in the second half.
"But to be able to play a game like we did, we had to make an enormous effort."
The Argentinian said Chelsea's quality had made life very difficult for his side, but he was impressed by his players' response.
"It's not easy to face these types of teams," he added. "If you take, for example the last game they played before they played us, the first proper chance that Chelsea conceded in that game was the 90th minute.
"So for us to have provoked five or six very good chances on goal has merit."