Bayern were desperate to beat Hanover to stay in the hunt for the second place that grants an automatic Champions League spot but the third defeat in as many games left them seven points off second-placed Bayer Leverkusen, who disposed of VfL Wolfsburg 3-0 to climb to 49 points.
Bayern club bosses had warned their Dutch coach second place was their minimum target but it was Hanover who were livelier, scoring through Mohammed Abdellaoue and Konstantin Rausch before Sergio Pinto added another after Arjen Robben had briefly pulled one back.
"My players were under a lot pressure going into this game," Van Gaal, in his second season at Bayern, told reporters. "After the first goal it got even bigger."
As for his future at the club, the 59-year-old former Barcelona and Netherlands coach said: "That is up to those in charge. I continue with my work but obviously after the third straight loss it becomes tricky."
Bayern's third straight defeat in all competitions, after their German Cup exit to Schalke 04 in midweek, left them in fourth place on 42 points, with Hanover third on 47.
Nuremberg's Christian Eigler scored four times as his team crushed St Pauli 5-0.
Bayern responded with Robben who headed in a Franck Ribery cross but a blunder from their keeper Thomas Kraft, when he failed to hold on Pinto's 25-metre shot, restored Hanover's two-goal cushion in the 62nd minute.
Leverkusen, with Michael Ballack asking to be excluded from the squad as he still lacked fitness, scored three times in the first half to quickly take the wind out of Wolfsburg's sails.
