The Heed visited Evo-Stik Premier side Buxton yesterday and edged them out 2-1.
Patrick McLaughlin scored the first goal of the Watson era and then Jordan Burrow added another from the penalty spot before half-time.
Liam Hardy netted a Buxton penalty but Gateshead held on to progress.
"We knew it was going to be difficult because the lad's confidence can't be very high after the run of results they've been on," said Watson. "It was a good time to get away from the league. I told them go out and express themselves and get their confidence back.
"I've been here a few times before with Macclesfield, it's a tough place to come and they've got some big, strong lads.
"We didn't win enough aerial battles and didn't communicate well enough, it allowed them chances which hopefully two weeks down the line won't happen.
"There were plenty of positives, like the amount of times we worked their keeper. The important thing for anyone in the cup is to get through to the next round."