The Manchester United boss left his star striker out of the last two games against Valencia and Sunderland, citing an ankle knock as the reason for his absence.
But, after playing for England on Tuesday Rooney - who is trying to rediscover his form after much-publicised allegations regarding his private life - then went against his manager's claims, denying ever having had such an injury.
Ferguson has since played down Rooney's comments - but former player turned pundit Mills believes Rooney should not have said what he did.
He told Sky Sports News Radio: "I think from Wayne Rooney it's naivety more than anything else.
"He's probably done it with the best of intentions, probably thinking that he doesn't want to use the injury as an excuse.
"But Sir Alex, I think, will be furious. Sir Alex is trying to protect his player as best he can - yes we all know that Rooney's got problems, not only on the pitch with form, he's had problems off the pitch as well - and Ferguson is the master at protecting his players, setting up a little cocoon around them, sending them off somewhere.
"And for Rooney to come out and basically just say 'Sorry Sir Alex, you're talking nonsense' I think its going to be very, very interesting, especially this morning and the next couple of days about that relationship."
Danny Mills talks to Sky Sports News Radio every Friday.