The result drops Bayern to fifth, but questions will be asked about their attack after Werder Bremen's Naldo was sent off after just a quarter of an hour, but Bayern still only left Bremen with a single point.
Bayern were without Italian striker Luca Toni, who scored two goals in their 5-0 Champions League hammering of Sporting Lisbon last Wednesday, and Klinsmann admitted his side took the foot off the gas in the second-half in Bremen.
"In the second half, we no longer showed the urgency you need to win a game like that," Klinsmann admitted with his side now fifth in the league. "However, we're not dissatisfied. Obviously, we'd have liked all three points, but going home with a point isn't a bad result, although it's only a small step forward. It was important to at least draw here. The title race will go to the last day. Obviously, we'd rather be a couple of places higher up the table. But we're on the case, we won't let up, and we hope we're top after 34 matches."
Bayern's former Bremen midfielder Tim Borowski agreed Munich did not do enough to test Bremen goalkeeper Christian Vander, who was replacing injured Germany goalkeeper Tim Wiese.
"We lacked an edge in front of goal," said Borowski. “We created a few good chances, but Bremen resisted well and had a good keeper, who made a number of great saves. We also didn't get the rub of the green at times."
Bremen coach Thomas Schaaf praised his side for their dogged determination despite the numerical disadvantage having knocked AC Milan out of the UEFA Cup last Thursday.
"After the red card, the team set out their stall for 75 minutes, refused to be beaten, and even created a chance or two. You can't ask for more than that," said Schaaf.
One player who was deeply satisfied with the result was goalkeeper Vander who reflected on a job well done.
"Taking a point with 10 men is always good for morale," he said. "It was a relatively easy game for a goalkeeper, you get to see plenty of action. I had quite a lot to do today. It was a terrific display, especially after the punishing game in Milan in the UEFA Cup, but we dug deep. We showed our fans we're all 100 percent committed to Werder."