Town sit four points above the Sky Bet League Two drop zone after Mickey Demetriou’s second-half free kick condemned them to defeat in South Wales.
The Glovers host Crewe Alexandra at Huish Park on Easter Monday (3pm kick-off) and Way insists his troops need to step up to secure three points.
“We’re bitterly disappointed but we have to move on quick as we have a massive game now,” he told YTFC’s official YouTube channel.
“I knew this weekend was going to be intense but the players need to regroup and we’ll look forward to the next game.
“I have to stay strong and make sure these players are up for the fight.
“They have to deal with the pressure. We’ve got a big game against Crewe now and I expect the players to show a willingness and a hunger to do whatever they can to fight for this football club.”
Tickets for Monday’s match can be purchased online.