Bayern scored twice in the second half, including Ivica Olic's last-gasp winner, after the visitors had taken an earely lead in the quarter-final first leg, to inflict United's first away loss in the competition this season.
"I am proud they were able to come back in such a way," said Dutchman Van Gaal.
"We were outstanding in the second half, we created chances and gave everything we had until the very end. Sweet is a good word for this win," he told reporters.
"I was not satisfied with the first minutes and then conceding a goal that early was a shock and we had to get back into our game plan and that is difficult. I am extremely proud of my players."
Bayern lost the 1999 Champions League final to Manchester United when the English club scored twice in the dying minutes to win 2-1.
Van Gaal, however, did not mention that game, which is among the most bitter memories for the Bavarians.
Instead he had only praise for his players, especially Franck Ribery, recently returned from injury, who levelled the scores with a 77th minute free-kick.
"For Ribery, it is just unbelievable what he did," Van Gaal said. "He has not played and suddenly he has to play at the highest level. I thought about substituting him because he had a lot of injuries."
Van Gaal said while United had grabbed an important away goal, Bayern would be no pushover in the return leg in Manchester next week.
"I think that Manchester United have a great chance after scoring an away goal. I wanted a 0-0 or a 1-0 win and 2-1 is not the best result. But we have scored at least one away goal in all our previous (Champions League) matches so we should have some confidence."
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