Solskjaer was permanently appointed manager in March after an impressive interim spell in the wake of Jose Mourinho's December sacking but seven defeats in nine games has raised doubts.
United was swept aside 2-0 by neighbour and Premier League champion Manchester City on Thursday (AEST), leaving the Red Devils three points adrift of the top four.
Ince – who won two Premier League titles and 10 trophies in total during his time in Manchester – criticised Solskjaer's approach and his determination to replicate iconic former boss Ferguson.
"Ole needs to get over Sir Alex Ferguson – he's the Man Utd manager now. We've tried this nice approach, the stuff about Ole giving the tea lady chocolates and trying to do what Sir Alex Ferguson has done," Ince wrote for Paddy Power.
"That's in the past now, we need to move forward from that. All of this 'Ole legend' stuff – yeah, he scored the winner in the 1999 Champions League final, we get that. But he's not a legend – he's the manager of Manchester United.
"Regurgitating how he's going to do it 'the Fergie Way' is pointless. It's doing my head in and I know others feel the same. Ferguson isn't the gaffer anymore – simple.
"No doubt he would help if Ole was in trouble, but I'm sick and tired of it, he's the manager, he has to forget about the past and realise Ferguson isn't the manager anymore, he is.
"I'm looking at the club and the future really worries me. They're a long, long way from many teams. Why did those players perform so well when Ole came in and now they're not? There's no character, no leadership, no desire, but the manager has to motivate the players too. These are the same players that were playing brilliantly a few weeks ago."
"I called it before he was made manager and got stick for it, but what I said was right," said Ince, who was sceptical of Solskjaer during his caretaker period. "I want him to be successful, but I don't think he's capable of doing the job. It's a huge rebuilding job. Will the players that are needed to carry it out want to come to Man United to play under him? I'm not sure. It's different to [Pep] Guardiola and [Jurgen] Klopp trying to attract players.
"The fact is, they should've waited until the end of the season before they gave him the permanent job. There was no rush to appoint him, but everyone got caught up in the euphoria and was thinking with their hearts rather than their heads.
"If you went to the board now and asked whether they should've given him the job – I think we know what they would say.
"Everyone jumped on the Ole bandwagon and now we're seeing the repercussions. Zinedine Zidane was available at the time and Mauricio Pochettino has always been the right man to take United forward in my eyes. Whether I'm wrong or right, I'm entitled to my opinion."