Sanchez replaced the injured Clement Lenglet in the first half and inadvertently turned the ball into Dominic Solanke's path for Bournemouth's second goal in the 51st minute.
The Colombian was booed by the home fans while being substituted by interim manager Cristian Stellini in the 58th minute.
"I've never seen this in my career," Lloris told beIN Sports. "I feel really bad for Davinson. He's a team mate, he's a friend and he's been fighting for the club for many, many years now.
"It's just sad. The story is sad for the club, for the fans, for the player. It's something you don't want to see in football."
Stellini took responsibility for the decision and vowed to support Sanchez.
"I thought it was early in the game to use a striker more because it was the first half and we were 1-0 up, so I didn't think it was the moment to change with a striker," Stellini said.
"Later, when we were 2-1 down I thought it was the moment. Davinson has to know it was only a tactical decision but we need to support him because it's a tough moment for him and also for all the team."
Saturday's defeat dented Tottenham's chances of playing in the Champions League next season, with the team fifth in the league with 53 points - three points adrift of fourth-placed Manchester United, who have two games in hand.
