The Vanarama National League club appealed the sending off in the first half of their game at Maidstone United on Saturday.
The Heed took their case to the Football Association on Monday but were told that the decision was to be upheld.
Vassell, 20, will now serve a suspension following the red card, the club have confirmed on their official website.
They will now have to do without the defender for this weekend's match against Boreham Wood.
Gateshead came from 2-0 down to secure a brace point on Saturday at the Gallagher Stadium without defender Vassell, a fightback which earned due praise from manager Neil Aspin.
The former FC Halifax now wants to draw a line over the incident ahead of their weekend fixture.
“Theo has been one of our standout performers this season but we will have to accept his suspension and prepare for Saturday’s game against Boreham Wood," he said.