I don’t believe that to be the case, he’s confirmed they tried to replace Lukaku and I don’t think for a second Ole would have been happy to let Lukaku leave without believing a replacement would be secured.
Selling your most prolific striker and not replacing them is never a managers decision, responsibility for that should be placed on Woodward.
Well you don't have to believe anything, this is what Ole said:
“If the right one [had been available], if it was there, we would have [signed a forward],” Solskjaer said. “It was time for Rom to go. He knows that. He didn’t want to be here. What is the point in having players that don’t want to be here?
“And there’s no point getting players in that you’re not 100 per cent sure about. When you get players in, you need the right ones that are going to stay here for a longer period and that’s the long-term thinking we have to show. I cannot think, ‘I need a player because this is my reputation’. No, it’s the club.
“There were strikers [available], but they weren’t the ones we wanted. We couldn’t get the one we wanted.”
Ole didn't want the strikers that were available so it is his responsibility the forward line is what it is.