Solskjaer took over as Manchester United manager after Jose Mourinho was sacked before Christmas.
The Norwegian has since own six games on the bounce against Cardiff, Huddersfield, Bournemouth, Newcastle, Reading and Tottenham.
The 1-0 Spurs win on Sunday was United’s toughest test and they came through it – in large part thanks to David De Gea’s impressive 11 saves in the second half.
Plenty of fans and pundits are calling for Solskjaer to get the managerial job full time, with his post currently set to end in the summer.
But Ince is adamant the Norwegian has done nothing extraordinary just yet.
“We can’t get too sucked in with what Ole’s done,” Ince told Paddy Power.
“Let’s be honest, it couldn’t get any worse at Manchester United before Jose Mourinho left.
“There was a dark cloud over the entire club, the players, the fans and the staff.
“It was impacting performances on the pitch.
“Ole’s come in, a friendly face at the club with a calming influence and it seems as though the players have upped their effort as a result.
“The shackles are off, but that doesn’t mean that Ole is the right man for the job.
“I could have gone in and done the same thing, so could Steve Bruce.
“Anyone could have gone in and done what he has done, it wasn’t a hard thing to do to give those players freedom and improve the mood.”
Ince has not managed a club since 2014, while Bruce is set to join Sheffield Wednesday in February when he comes back from holiday.
As for Ole Gunnar Solskjaer, he is still under contract at Norwegian side Molde and is expected to return to the club in May when the Premier League season ends.
The 45-year-old is one of a number of candidates United’s board are looking at as a long-term successor to Mourinho, however.
Spurs boss Mauricio Pochettino is on that list, while Laurent Blanc and Zinedine Zidane are currently out of work.
Antonio Conte could be another option for United after he was sacked by Chelsea in the summer.
Conte still has six months remaining on his £9m-a-season Chelsea contract, meaning United were unlikely to move for him after sacking Mourinho.
The cost of covering that contract was also what put Real Madrid off, with Santiago Solari currently in charge of the first team.