United went down to an Ollie Watkins goal at Old Trafford. They start their Premier League campaign a week late after their involvement in the Europa League until the semifinal stage.
Central midfielder Van de Beek, who joined United on a five-year contract from Ajax earlier this month, stood out in the loss.
"Donny was maybe the biggest plus in the outfield," Solskjaer told MUTV. "He's such a finder of space and he creates time for himself with his timing and movement. I was very happy with his performance."
"I thought Deano showed his authority back there and he played like a proper Man United goalkeeper," Solskjaer said. "And especially in the second half, you saw Teden when he came on, how exciting a prospect he is."
Several other young players were involved for United, including Ethan Galbraith, James Garner and Anthony Elanga and Solskjaer was happy with their involvement.
"They'll learn from it of course," he said. "Young Ethan Galbraith has been with us in the summer, in the Europa League, he's been training with us and then he gets minutes today and you could see he's got less time [on the ball].
"I spoke to him after the game and he knows a couple of times he gets caught on the ball but that's the learning he needs. That's going to make him, next time he's on the pitch, be ready for it."