Van Persie appeared as pundit for the clash between his two former clubs, alongside ex-United defender Rio Ferdinand , and was critical of Solskjaer's demeanour after the defeat.
"When I listen to Ole, he sounds like a really nice guy," van Persie said on BT Sport. "I would like to see him a bit more mean at times, just be angry.
"I see him smiling now after a game like that. This is not the moment to smile."
Van Persie suggested the blame for last night's defeat should lay at the manager's door.
"They need a gameplan and a bit of fear for the coach," he added. "You know if you don't make those runs or make that pass, you will be punished and you won't play the next game."
When asked if United players lacked fear, he replied: "Probably. By the looks of things, I think so."