United crashed out with a 3-2 defeat at Wolfsburg, who made club history by reaching the knock-out stages as Group B winners.
PSV Eindhoven's 2-1 win at home to CSKA Moscow allowed the Dutch to claim second place at Manchester's expense as third-placed United now drop into the Europa League.
The Red Devils suffered a repeat of their 2011/12 European campaign when defeat in their final group game at FC Basel also denied them a place in the last 16.
"I can't defend myself, because we are out of the Champions League and every word I say will be wrong," he said with United fourth in the Premier League table.
"But when you see the facts, we qualified for Europe last season and we are in a good position in the league. The facts say we are better than last year.
"I can only give facts, but of course I am disappointed that we are out of the Champions League."
Anthony Martial's early strike for the Red Devils was cancelled out by first-half goals from Brazil's Naldo and Portugal's Vieirinha.
United drew level when Wolfsburg's French midfielder Josuha Guilavogui scored a late own goal seconds before Naldo claimed his second by heading the winner.
"It was a crazy match," said Van Gaal. "We twice gave away goals within two minutes after we had scored, that was difficult to understand.
"I am happy that we scored, but I am not happy why we defended so poorly and it's something I have to analyse. I've said in advance this was a tight group and you see it in the results we had.
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