Former United midfielder Ince tempered some of the enthusiasm surrounding the Norwegian's winning as start as Old Trafford interim manager by saying things "couldn't have got any worse" after Jose Mourinho.
He claimed he or former United team-mate Steve Bruce would have had similar success following on from the sacked Portuguese.
And former Liverpool defender Carragher says that is worthy of praise, adding that the 1999 Treble winner has given United their swagger back.
"A lot has been written about Solskjaer and everything being very, very positive on the surface," he told Sky Sports.
"I think underneath that, a lot of people were looking at it before the Spurs game and thought: 'Anyone could have gone in there and done that'. It's nonsense. It's absolute nonsense.
"He's made big decisions by leaving people out – [Romelu] Lukaku, an £80 million striker, on the bench. When he's brought him on he's made an impact.
"You think of Jose Mourinho, people were saying these games were easy. Last season, when Manchester United finished second and got to an FA Cup final, Mourinho lost three games to promoted teams.
"So it's not easy to go and wipe the floor with these teams. He's [Solskjaer] made a great start to his career."
United's confidence is back, too, according to Carragher.
"It felt like the fear had gone from Manchester United," he added.
"For three or four years, watching Mourinho away in big games, Manchester United were terrified going into them thinking they couldn't compete with these other top teams."
United face Brighton at Old Trafford on Saturday as they look to continue their charge towards the top four. Indeed, the Red Devils are now level on points with fifth-placed Arsenal after the win over Spurs at Wembley.