A 90th minute strike from Jon Dahl Tomasson gave Milan a strong lead for next week's return after European Footballer of the Year Andriy Shevchenko had put them ahead just before the interval but PSV had earlier spurned a series of chances.
"At 1-0 it would be more possible but now it is difficult," said Hiddink. "But the lads were saying in the dressing room that next week we are not going to surrender."
Hiddink, who orchestrated one of Italian football's worst nights when his South Korea team eliminated Italy from the World Cup in 2002, was exasperated by PSV's defeat.
"There were large parts of the second half where we were so dominant and, of course, if you have such control than it is very frustrating to get a result like this," he added.
VITAL MOMENT
"It is one thing if you are simply blown away by a major powerhouse but if you are superior like we were after the break it is frustrating," he added.
"We showed we can play and play against the best. Then right at the end, when they were not playing well because of all our domination, they scored at the vital moment. We were so close.
"I'm proud of the boys for what they produced against a club with over five times our budget but you always like to win," Hiddink said.
The Dutch coach rued the inability of his team to put away their chances.
"It's not easy to come here against one of the best organised defences in the world and create six good chances. But when you do that you have to score at least one.
"That was probably the difference -- they took their chances, they were deadly inside the box," he said.
Hiddink knows it will now require a major upset for his team to make it to the Champions League final in Istanbul on May 25.
"It's difficult to be honest. They will wait for us and not try to dominate the game and they will look for the counter attack."
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