Playing in front of United supporters for the first-time, Cavani produced a 40-yard lob to give his team a first-half lead.
And Solskjaer says there will be many more to come from the Uruguyan.
Speaking after the game, Solskjaer said: "How good was Cavani's goal? Oh, top.
"That was the highlight obviously. What a way to introduce himself to the Stretford End.
"I know I've said it a long time, but we need fans here and they're going to see him score many goals for us. That was an excellent finish, and the way he works to get his chances as well is exceptional."