Lloris suffered a horrendous elbow injury in the 3-0 Premier League defeat at Brighton in October.
"It is not nice to see someone you appreciate so much leave," said club captain Lloris of Pochettino.
"But you also know it is part of football. But it is not for the players to have a say in that. You must immediately be at the service of the new coach."
On Mourinho, the French goalkeeper also told L'Equipe: "It is a chance for the players to work on a daily basis with one of the greatest coaches of the last 20 years.
"He has won everywhere. He has a precise mission for the one thing that has been missing – a trophy."