Bayern are up to ninth in the table after Friday night's draw, but remain nine points behind leaders Dortmund who host Hoffenheim on Sunday.
German giants Bayern were seeking a first win in Hamburg for five years but they settled for a point without captain Mark van Bommel, defender Daniel van Buyten, striker Miroslav Klose, plus playmakers Arjen Robben and Franck Ribery.
"I went to the dressing room after the game and told my players it's a shame we didn't win," admitted Dutchman van Gaal.
"I have the feeling we could have come away with a lot more than that. Hamburg were physically shattered in the last 15 minutes, which is basically when we should have been scoring the single goal we needed. We failed, and we could even have lost it as well."
Hamburg could have taken all three points right at the end of the game when Burkino Faso midfielder Jonathan Pitroipa beat the defence and curved his shot around Bayern goalkeeper Hans-Joerg Butt, but his effort hit the post.
"Obviously, we wanted to come away with the three points, but Hamburg had a huge chance to win it at the end, so we have to be satisfied with a point," said Munich captain Philipp Lahm. "After all, HSV aren't just any old team. Overall it was a reasonable performance, but we need more determination and precision in the final third."
With his side fourth in the table before Saturday and Sunday's matches, Hamburg coach Armin Veh said he was happy to take a point off Munich. "Bayern were missing a few players today, but they still boast enormous quality," said Veh.
"It means you can't spend the last 20 minutes throwing everyone forward, you have to make sure you're not hit on the break."
Hamburg captain and Germany defender Heiko Westermann rued his side's missed opportunities, especially Pitroipa's effort which had home fans clutching their heads in agony as his golden chance went begging.
"We had the better chances and could have won the game," said Westermann. "It's a real shame Pitroipa didn't score, and (Piotr) Trochowski was in a one-on-one with the keeper too. But one point is better than none."