An early goal from Macaulay Langstaff gave Williamson’s men a narrow half-time lead but second-half strikes from Adam Campbell and loanee Taylor Charters eased Gateshead to all three points.
They now head into a tricky looking visit to Alfreton this weekend with Williamson’s words of warning fresh in their minds.
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He told The Echo: “Unless you’re telling me promotion is handed out in February, it doesn’t matter where we are right now.
“It means nothing, it just means you have a target on your back and more noise surrounding what is going on.
“The lads are very good and now we are just focused on a massive game at Alfreton this weekend.
“It’s about getting our recovery right and making sure we get that side of the game right,” he added.
Williamson reflected positively on a long-awaited win over Spartans after two defeats and and two draws in their last four games against their local rivals.
The former Newcastle United defender admitted Terry Mitchell’s men were always in the game until Charters’ late strike - but praised his own players for their positive reaction to Saturday’s home defeat against fellow promotion contenders AFC Fylde.
“I don’t think I would describe it as comfortable - but when the third goal went in, it relieved a bit of pressure on us,” explained the Heed boss.
“They have some very good players, and as much as we dominated the majority of the game, they were still always in the game when they have that attacking threat.
“I am delighted for the boys, they really deserve it and it felt like we were on the end of an undeserved 3-0 defeat on Saturday, so they’ve shown character to react to that in the right way,” he added.