Mourinho afterwards said he "did not like his team", adding: "In the second half we were poor and in my opinion we were not physically strong, no intensity. The team lacks in this moment many players’ physical condition.
He said: "We didn’t press because our pressure up front was very, very poor ... Lazy pressure up front, that creates an unbalanced situation for the rest of the team. It disappoints me and that is where I now have to work."
Mourinho has pointed to a disrupted pre-season, with a truncated break, international matches and positive Covid-19 results.
But former Manchester United goalkeeper believes Mourinho pointing the fingers at his players' work rate could severely backfire and result in "ruin".
"Going back to the time when I was playing, in the '90s specifically, there were a lot of managers who always used to say 'you never have a go at your players publicly because you can lose the dressing room'," Bosnich told Sky Sports.
"That was with the type of character you had back in those days, which was different, let alone these days.
"When I heard [Mourinho's comments] I was like 'that's a huge risk' because, unless he knows he will be 100 per cent secure no matter what he does or says, I don't think that would be the case.
"It was a disjointed performance yesterday from Spurs and Everton, obviously, played really well. Richarlison would have had a hat-trick on another day.
"On Spurs, I don't sense everything is completely hunky-dory when you've got the manager coming out saying things like that.
"He might be looking for a different type of reaction but if you lose a big player, that will bring with him another four or five players from the dressing room and that could be a road to ruin."
It's not the first time Mourinho has called out his players, having questioned their mental strength following a 3-1 defeat at Sheffield United late last season.
He said at the time: "Clearly if these boys don't care about results and don't care about the position we finish at the end of the season we'll be in big, big trouble for the future."
Spurs went unbeaten in their final six matches of the campaign, winning four, following the defeat at Bramall Lane.