Koeman impressed during his two-year tenure on the south coast, but incurred the displeasure of the Saints faithful by departing for Goodison Park in the off-season.
And while more than a few boos can be expected, the Frenchman hopes the crowd will not be too harsh on the former Barcelona player when he returns for the Premier League clash on Sunday.
"He did very good work at Southampton and last season helped the club to play European games. This is very important. I have a lot of respect for him and for his work," Puel said.
"Of course he deserves a positive reaction. The fans are excited to see their former trainer, it is important to respect him and his work here.
"Now though, we should consider the game against a strong team and not just the comeback of Koeman. We want our fans to be behind their team and this is the most important thing."
Southampton head into the game just three days after a 1-0 defeat away to Sparta Prague in the Europa League, and Puel acknowledged the challenges of remaining competitive with such a hectic schedule.
"It is always difficult to play after a Europa [League] game because of the [short] break you get after the game," he said.
"You only get two days to prepare and you get one less day for recovery from the Champions League.
"But we are happy to play these games, we have to adapt to this situation. We need to show our character and quality to get some points."
The Frenchman also offered an update on the fitness of two key players in Jose Fonte and Dusan Tadic.
"Jose I believe can play, but Dusan no. Now he's two weeks without a training session and at the moment it is difficult for him."