The Glovers progressed to the last 16 of the latter with a 4-1 win over League One side MK Dons, thanks to second-half goals from Dawson, Francois Zoko, Alex Lacey and Ben Whitfield.
Darren Way’s side have now scored nine goals in their last two matches – both at home – and are unbeaten in eight matches at Huish Park.
“It was very important to keep the momentum going,” Dawson told YTFC’s official YouTube channel.
“We didn’t want to undo our good work on Saturday (5-0 win over Crawley Town) and change the positive vibe.
“We can carry that on now and obviously it’s a massive game on Saturday.”
Yeovil are in home action for the third time in a week when Barnet head to Somerset this weekend.
Town could make it eight league matches unbeaten and Dawson hopes their recent performances will entice more fans to the match.
“We’d love a big crowd,” he said.
“The fans have been suffering for a couple of years, we know that, but we’re trying to put it right every game.
“I think we’re doing that at the minute so hopefully we can get a big crowd on Saturday.”
Fans can purchase tickets for Saturday’s fixture in person at the ticket office, online or by phone 01935 847888.