"It is the man who decides who the referee is who is to blame. A man like that [Geiger] should not be put in charge of a game of that magnitude.
"With all due respect, Pierluigi Collina, as the man who designates the referees, he is very bad. He must apologise to the Colombian people.
"I told [Fifa president] Gianni Infantino that, if I worked for Fifa, I would change everything. It has to be transparent. That's why I didn't go there.
"The referee will know a lot about baseball, but he has no idea about football. The Colombian players asked for VAR [Video Assistant Referee intervention] and he did not give it to them.
"Twice, the English threw themselves to the ground and he did not admonish them. This was theft."
In an ill-tempered match Geiger struggled to control, England took the lead when Kane was bundled to the ground by Carlos Sanchez.
Maradona said: "The penalty was not a foul. In fact, it was Kane's fault.
"The referee is looking somewhere else and when he turns his head, Kane is on the floor.
"Kane used his arm to hook Sanchez and then threw himself down.
"I repeat, why didn't the referee ask for the VAR? Colombia died standing. That's why I applaud them."
The Telegraph approached Fifa for a response.
Immediately after Tuesday's game, Colombia captain Radamel Falcao accused Geiger of being biased in favour of England.
"I found it peculiar that they put an American referee in this instance," Falcao said.
"To tell you the truth, the process leaves a lot of doubts. He only spoke English. Some bias was certain.
"The referee disturbed us a lot. In the 50-50 plays, he always made the calls in favor of England. This situation was undermining us. He didn't act with the same criteria for both teams.
"When in doubt, he always went to the England side. It's shameful that this happens in the round of 16 of a World Cup."
Geiger's tournament also began in controversial circumstances after he was accused of asking for a Portugal player's shirt during their 1-0 win over Morocco, an allegation Fifa condemned as false.