After finishing sixth in the Vanarama National League, they had qualified for a spot in the play-offs.
However, the club had to comply with specific terms within the EFL rules.
A statement from the governing body read: Gateshead Football Club will not be permitted by the National League to participate in this season's Play-Offs as the terms of the Club's occupation at the Gateshead International Stadium, owned by the Borough Council of Gateshead, does not meet the relevant qualifying criteria to enable the Club to become a Member of the EFL.
All other Clubs permitted to play in the National League play-offs adhered to the requirements as set out in EFL Regulations.
Despite the League working with Gateshead throughout last season and again in recent months, the Club has been unable to attain security of tenure to play matches at its Stadium for a minimum of 10 seasons.
All National League Clubs are required to apply annually to the EFL should they wish to be eligible for promotion, which Gateshead did alongside other Clubs by the 30 November deadline. Working with the EFL, Clubs then had until 1 March to ensure that all the relevant criteria of EFL Regulations were met."