The Welshman scored his first goal for the club to make the score 2-1 before the hosts raced to a 4-1 lead.
Francois Zoko’s strike acted as a consolation leaving the experienced Lawless to want to confirm safety against Stevenage next weekend.
“That’s something we’re aware of as a team (not being mathematically safe) and we want to put that to bed asap.
“It’s going to take hard work and a response after that against Grimsby.
“We’re thoroughly disappointed and have let a lot of people down and it’s going to hurt. But I’m sure that hurt will fuel some revenge.”
With the score at 3-1, Grimsby’s Scott Vernon made it 3-1 from a corner which left Town stopper Jonny Maddison appealing for a foul as the ball swung into the box.
Referee Eddie Ilderton saw no wrongdoing, leaving the Glovers with a mountain to climb once again.
Despite the setback, Lawless feels both Maddison and the whole side will learn from the performance.
“From where I was standing I thought it was a foul, but the referee was adamant there wasn’t anything there.
“Jonny is a strong-minded lad and we’ll all learn from these things, not just Jonny.
“We have to learn very quickly as well because it’s four or five days later (since beating Crewe 3-0) and it’s poles apart.
“We’ve got to learn very quickly.”
Yeovil now host Stevenage at Huish Park next weekend with another chance to confirm mathematical safety, something the Town midfielder is confident can be done despite the setback in Lincolnshire.
“It’s massive,” he told YTFC’s official YouTube channel. “We wanted to do that today so nothing has changed there.
“We performed well at home on Monday in front of a home crowd and now we’ve got to do it again, we really have, and I have no doubt we will.”