Dortmund were impressive, particularly in the first half, but could not find a breakthrough before being forced to defend against Bayern's sustained attacks after the break at Signal Iduna Park on Saturday.
A win for second-placed Dortmund would have seen the gap at the top of the Bundesliga close from five points to two, but Tuchel was happy to settle for a share of the spoils.
"I want us to pick up as many points as we possibly can. Next we face Tottenham, then Mainz. Even if we had beaten Munich today, we would still be behind them in the table, albeit by only two points, and we still have an inferior goal difference," the Dortmund coach said.
"We must stay hungry and impassioned. We shouldn't be disappointed with today's 0-0.
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"We played a very, very good first half, and an especially outstanding 30 minutes at the start. I enjoyed instructing the team from the side.
"A goal to take the lead would have helped us a lot, of course. I am very satisfied with the team's performance today.
"It is very difficult to endure a period of sustained pressure from Bayern. It was important to remain disciplined in defence today.
"The Bavarians play at an extremely high level. You have to defend very well accordingly. We never lost our shape though, and were never passive in pursuit of the ball.
"We could have controlled the ball better in the first half. We were a bit too rushed, too imprecise. However, we remained competitive and never lost faith."
Dortmund are at home to Premier League title challengers Tottenham in the first leg of their Europa League round-of-16 tie on Thursday.