Harry Kane had given Spurs the lead in Eindhoven after Lucas Moura cancelled out Hirving Lozano's opener in the Group B clash.
But Lloris' 79th-minute red card gave PSV a chance, and the hosts capitalised through Luuk de Jong's equaliser.
However, Pochettino said there was no reason to blame Lloris, who brought down Lozano with a rash sliding challenge outside the area.
"I'm not going to blame any player. If someone wants to blame a person, it's myself to blame because I am responsible for the team. We didn't win," he told a news conference.
"If someone wants to blame someone blame me, not the players. The players are there to play and perform in the best way. Sometimes it's difficult.
"The problem is when you are so, so good, when you play much better, dominate the game and create the best chances and if you can't kill the game, the game is always open and with some action you can concede a goal or a chance like we conceded, an accident for Hugo and the decision didn't help us.
"Of course you draw and it puts our qualification for the next stage of the Champions League in a difficult situation."
Asked if Lloris had apologised for his error, Pochettino said it was unnecessary for the shot-stopper to do so.
"No, no, no, no. One day when I was very young one manager said to me you don't need to apologise after I made a big mistake, because only the player on the pitch can make a mistake," he said.
"If I am sitting here, sitting in the dugout, it's difficult to make a mistake. Football is about making mistakes.
"But in that case it wasn't a mistake, it was an action that happens a lot in football and is a sending-off.
"Hugo doesn't need to apologise to myself or the team. It is an action that happens often and sometimes football is like this."