The 34-year-old scored two excellent goals in 3-2 loss, which saw United advance to the Europa League final due to an 8-5 win on aggregate.
And Solskjaer believes it is easy to see why the club want Cavani to extend his stay at Old Trafford beyond this season.
"The reason we're here is because we've got a centre-forward who has scored four goals during the tie," Solskjaer said.
"Edinson has shown again why we want to keep him at Old Trafford.
"Football has its own language. Edinson has proven tonight, in previous games and throughout his career what a centre-forward should be doing both on and off the ball, both preparing for games and recovering from games."