Jerome Greaves (two) and Ryan Qualter were on target as the Gladiators claimed three Northern Premier League points.
"We huffed and puffed a bit," head coach Shaw reflected.
"We created our best chances when we were brave enough to play.
"We came to slow the game down a little bit. I thought there'd be a few tired bodies (after Saturday's win against Whitby)."
Shaw is now calling on his side to be more defensively switched on.
"Ultimately, if we don't head the ball in our penalty box we'll lose football matches," he added.
"Three first contacts and we've lost 3-0. They've not carved us open at any point and we've had good opportunities from some good play that's sliced them open.
"Disappointing result because we've not defended our penalty box well enough against two big centre forwards.
"We've got to take our learning from that and get miles better."
Trinity travel to Sporting Khalsa in the FA Cup on Saturday (KO 3pm) and entertain Morpeth Town in the league on Tuesday (KO 7.45pm).
Shaw believes his side’s first victory of the season can be a catalyst for more success.
Toby Gould netted the only goal of the game to beat Whitby Town at the Northolme on Saturday, as the new boss and his newly-assembled side put some frustrating results behind them.
“Very pleased. I think we’ve probably deserved a few more points than we’ve got on the board from the two home performances before this,” Shaw said.
“Delighted to get a win, probably gives people a bit more belief. They’ll puff their chest out now and know they’re a good team. You can see the potential of the group.
"You can see how good we can be but those moments are really important - the first win, the nature of the win.”
Gould tapped home the only goal of the game in the 16th minute after good work from Nyal Blake, sparking celebrations on the terraces and in the Shaw household.
“It’s my dad’s birthday and my daughter’s birthday today, so I’ll dedicate it to them,” he added.