Although Spurs ultimately ran out comfortable victors, they arguably could have won by even more had Son been awarded a penalty in the 16th minute.
The South Korea international went tumbling in the area after an attempted tackle by Harry Maguire, but referee Oliver showed him a yellow card after deeming he had dived.
It had little impact on the end result, even if the scoreline flattered Spurs, but manager Pochettino was infuriated by the incident.
Speaking to reporters, he said: "Do you think that Sonny deserved to be booked?
"Unbelievable, unbelievable, unbelievable. When you compare the situation with the penalty against us, unbelievable.
"The problem is, I told Michael Oliver the situation of Liverpool in the last minute that should be a penalty [Son was brought down by Sadio Mane], to maybe be 2-2, maybe 2-1, but it was a clear penalty.
"It was the same referee, but now I don't know how he has measured the situation. It is so difficult. I am a person that always accepts the mistake, but I think it was so strange the situation.
"It was so clear the position [Sunday] with Sonny, the action, but it wasn't clear the position of [Leicester's James] Maddison when he was on the floor.
"I think it is unbelievable. I am more relaxed because we won the game, three important points we got, but so disappointed with the situation because everyone wants to talk about different clubs or players, but do you think we are a team that is trying to cheat the referee?
"Come on, we are the most innocent people on the pitch."
Son eventually notched a 91st-minute goal to secure Spurs' win and take them within five points of Liverpool and Manchester City, with the Champions notching a 6-0 victory over Chelsea later on Sunday.