The former United striker was unhappy with Solskjaer's post-match response to defeat at Arsenal, believing he was "too nice" with his reaction.
However, Solskjaer responded on Friday: "I don't know Robin, and Robin doesn't know me.
"He probably has no right to criticise my leadership style, and I'm not going to change my mind. That is for sure.
"Robin took my shirt number 20, and that's probably the only thing he's going to take away from me too. Because I don't live in the middle ages."