The Argentine has left St Mary's after 16 months at the club to take up the vacant managerial post at Tottenham Hotspur.
Le Tissier, who spent the majority of his playing career at Southampton, told Sky Sports News: "Mauricio has done a pretty good job there so it is a bit of a blow, but you have to look at it positively, this is a chance for another manager to come in and inherit what is a very stable football club.
"We may lose one or two players but there should be funds available for a new manager to come in and build a new squad, so we go again.
"This football club has sold many players down the years and has been written off many times, yet we have still come back and we were eighth in the Premier League last season, there is no reason we can't do it again."
Southampton finished eighth in the Premier League in Pochettino's first full season at the club.