Henderson made a crucial stop on his club debut to maintain United's 1-0 lead in the second half, before they went on to add late goals to win 3-0.
Solskjaer said: "I'm very pleased with his performance both when he had to make the save and also how he voiced the team. And when he's got the ball at his feet he's always comfortable."
Marcus Rashford and Mason Greenwood added gloss to the scoreline and the Norwegian coach was pleased to see the pair open their accounts for the new campaign.
He said: "It's great for them to get minutes as well but also goals. I think the first one [scored by Rashford], I like that goal because the ball goes forward and it goes quick. It's not perfect but Mason gets hold of it, leaves it for Marcus and you can see that he's composed in his finishing.
"And Mason, you see his chance there, he can go inside, he can go outside, he had one other one before when he went with his right, now he went with his left. Of course, it's great for them to get off the mark."
Henderson added that he had been dreaming his entire life of playing for Manchester United.
In a Twitter post after the match, he wrote: "I dreamt about this my whole life!! Unbelievable feeling to make my debut for the club I love!! Clean sheet and a win to top it off!!!"