Colombia were beaten 4-3 on penalties after the sides were locked at 1-1 following 120 minutes of play in Moscow.
England had opened the scoring with a Harry Kane penalty after Carlos Sanchez was penalised for obstructing the Tottenham striker in the box.
However, replays appeared to show Three Lions captain Kane pulling Sanchez down to his midriff to initiate the move.
It is one of two incidents, along with a disallowed Carlos Bacca goal, highlighted by the petition.
The petition, which is edging closer to its 300,000 signature target, calls on FIFA to review the decisions to "set a precedent for fair play, where good play prevails".
Mateus Uribe and Bacca were unsuccessful from the spot for Colombia in the shoot-out, opening the door for Eric Dier to fire England into the quarter-finals with the winning penalty.
After the match, Colombia captain Radamel Falcao hit out at the officiating, telling reporters: "I found it peculiar that they put an American referee in this instance... to tell you the truth, the process leaves a lot of doubts.
"The referee disturbed us a lot, in the 50-50 plays, he always made the calls in favour 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."
England meet Sweden in Samara on Saturday with a place in the semi-finals of the tournament up for grabs.