Real Madrid had no such trouble as Cristiano Ronaldo scored a hat-trick in a 4-0 thrashing of 10-man Shakhtar Donetsk yesterday.
Paris Saint-Germain, Juventus and Atletico Madrid also began with victories.
But the main talking point in the Netherlands was Shaw's terrible injury that saw him taken to hospital, and will now require an operation.
"It's horrible. When he was going in the dressing room, he was with the oxygen mask, he was crying," said United manager Louis van Gaal.
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The England international was surging into the box when he was crunched by a dangerous tackle from Mexico international Hector Moreno.
"I'm really sorry. I think I played the ball," said Moreno. "I just hope he'll be back as soon as possible."
Shaw received treatment for eight minutes on the pitch.
Memphis Depay gave United the lead against his former club with a sublime goal on 41 minutes.
If that equaliser was against the run of play, PSV's second had an element of smash-and-grab about it as Luciano Narsingh headed home a deep cross from Maxime Lestienne.
United dominated in terms of possession, territory and chances but simply could not find another goal.