The Argentine’s position was the subject of uncertainty after chairman Nicola Cortese left the club this week.
However, Pochettino confirmed yesterday afternoon that he intends to stay.
“I think that was important,” said Le Tissier. “We have had enough changes of manager, so I think it was important for the stability of the club that the manager stayed, and I think it was important to the players as well that the manager stayed.
“It sends out a good signal to the players that things aren’t falling apart.”
As for what he thinks needs to happen now, Le Tissier added: “I think firstly the fans would like some reassurance, which Mauricio has given a bit, so that was good, in terms of saying players are not for sale as well, although he deflected the Luke Shaw issue back onto the owner.
“The most important thing is that the fans stick behind the team and hopefully the Liebherr family don’t want to sell up straight away, which I think is the main worry for everybody.”
The Saints legend insisted he was not shocked by this week’s sudden departure of Cortese.
“I’m not overly surprised,” he said. “Obviously, something was going on with what happened in the summer and it always seemed to be a pretty tenuous relationship that they had there.
“The fact Franny (Benali) got a phone call 10 days ago saying he was welcome back at the club, I thought there must be something wrong. We won’t ever really know what’s gone on, though, because all we get is (Cortese’s) PR, and the Liebherrs don’t make any comments in public.”
Le Tissier also addressed the issue of the week’s events on his internet blog.
“There will probably be a lot of fans, who are only concerned about what happens on the pitch, who will think this is bad thing for the club, which is quite understandable.
“But I think anybody who’s had any dealings with the man [Cortese] will think completely differently.
“A lot of them will think “Good riddance” to be honest because he upset quite a lot of people with the way he conducted his business.
“We had our own differences of opinions but I didn’t lose any sleep over it.
“The fact he’s actually chosen to walk away at a fairly crucial time in the transfer window, with a couple of weeks left to strengthen the squad, proves he didn’t have the best interest of the club at heart.
“It was always a case with him of having the best interest of Nicola Cortese’s heart.
“If he had gone about his business in a different way he would have been a huge hero with everybody.
“It was a shame that there were bits he did off the field that he kind of spoilt when everything else was going so well.”
l Le Tissier’s blog features on the goaldengoals.co.uk website.