The Slovaks were forced to play the final 33 minutes with 10 men after Martin Skrtel was sent off having received two yellow cards, both for fouls against forward Harry Kane.
Questioning Serbian match official Milorad Mazic's decision to give Skrtel a second yellow card, Durica claimed there is a wider conspiracy to ensure England qualify out of Group F.
"There is only one place at the World Cup. Why should Slovakia go there when we have England in the group?," Durica was quoted as saying by skysports.com on Tuesday.
"Of course, they will always prefer the stronger team. Probably, the referee exactly knew how to do it," the Trabzonspor defender added.
"Today we might have played more than England."
Skrtel's dismissal meant Slovakia played more than half an hour with 10 men in the game, which England won 1-0 through Adam Lallana's injury-time goal.
"And it was after a really strict red card. I think that the referee waited until Skrtel did a foul. We were really unhappy," Durica, who has played more than 80 international caps, said.
"Englishmen knew that they are one player more, so, logically, they began pushing forward and creating the pressure. But they did not have clear chances, so that is why we regret it, the 34-year-old added.
"If they would have created some great action and scored nice goal, you say it is okay, but not such as goal in the stoppage time."
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