At the end of the game, Mourinho had stayed out on the Old Trafford pitch applauding the remaining United supporters, also brandishing a club scarf.
The former Chelsea boss has made clear his displeasure at United's lack of activity in the transfer window, but his side were blown away by a Spurs team that did not make a single signing.
And Bosnich – who won the Premier League title at United in 1999-2000 – thinks Mourinho would be better off adopting the approach of Pochettino, who has been touted as a possible successor to the Portuguese.
"It really shocked me. What transpired in that news conference was concerning," Bosnich told Omnisport.
"I'm a Mourinho fan and always have been. But what happened at the end of that news conference wasn't a good look for him, the club or anyone.
"There's obviously been problems behind the scenes with transfers, but he works for the club and the club doesn't work for him.
"If they have decided not to spend money, he really needs to take a leaf out of Pochettino's book and get on with it."
But Bosnich believes Mourinho can get United back on track despite a sticky spell that has seen speculation grow that he may be on his way out.
"I don't think they will win the title, but they are more than capable of challenging," added Bosnich. "They did come second last season, even if it was 19 points behind. He needs to just summon up all the powers he has and get the best out of those players.
"The majority of players have been there because he signed them. He is obviously trying to make a point that he wants new players. Just like a battle with a manager and a player, 99.9 per cent of the time the manager is going to win. A battle between a manager and the boss of a club, 99.9 per cent of the time, the club is going to win.
"He signed a new contract and there's a long time to go. He needs to sit down and decide what he really wants to do.
"If it is that he's had enough, well he knows what he needs to do, he's been around for a very long time."