The Mariners had worked alongside a number of other clubs across the Non-League system to challenge the decision that was officially ratified by the FA Council in April.
Thompson attended a hearing with a three-man council earlier this month and was told that the bid had been unsuccessful seven days later.
In a somewhat cruel twist of irony, the news was announced on the same day that the EFL revealed that they would promote and relegate League One and Two clubs on a points-per-game basis.
Had that method been implemented in the Northern Premier League’s top tier, South Shields would have secured their fourth league title and promotion in the last five seasons and joined north-east neighbours like Gateshead and Darlington in the National League North.
Mariners supremo Thompson admitted that the lack of consistency in the decision-making across the football pyramid made the decision to reject the legal bid even more difficult to understand.
He told The NLP: “It’s difficult, but we have to respect the outcome.
“We had some very senior people listening to the arguments.
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