Koeman was appointed the Southampton manager in the summer of 2014, and after two years, the Dutchman left for Everton in the summer of 2016.
"I said at the time that I was surprised that he almost made a backwards step," The Liverpool Echo quoted Le Tissier as saying in November 2016.
"I think it's going to be tougher for him at Everton than he thought. No disrespect to Everton but I thought he could have got a bigger move given the great work he did at Southampton."
Everton are set to finish seventh in the Premier League this campaign, and Southampton legend Le Tissier has claimed on social networking site Twitter that this shows that leaving the Saints for the Toffees has been a step down for the Dutchman.
RK finished 6th last season 7th this season, thats a step down isn't it https://t.co/ph8rDDVh5V— Matt Le Tissier (@mattletiss7) 18 May 2017
blues (@eternalblue1878) 18 May 2017
Southampton could end up eighth in the Premier League this season, but there is a massive point-gap between them and Everton.
The Toffees are an ambitious club, and the Merseyside outfit will be aiming to push for the Champions League places during the 2017-18 campaign.
If Koeman signs the right players in the summer transfer window, then Everton could be genuine contenders for a top-four finish in the Premier League next season.