Shields are flying high at the top end of the table and despite Alex Wollerton giving Trinity an early lead, the hosts hit back to take the points.
But Shaw wasn’t too downhearted with what he saw from his team, even if that wasn’t the case all round.
He said: “I’m frustrated and quite angry about things that went on in that game that were nothing to do with Gainsborough Trinity players, staff or supporters who I thought were very good.
"The game shouldn’t have ended with that scoreline. We had a long time in their half and lots of chances and South Shields haven’t, so to come away having lost 3-1 is something I’ll have to pick the bones out of football-wise.
"There was definitely a script today for who should win. You’ve got a team whose two centre-forwards are earning more money than the other team can pay their squad, plus there’s a good crowd and a good atmosphere.
"We did our absolute best to spoil that but everyone else wanted the outcome people thought should happen.”
From a playing perspective, Shaw was delighted with his side’s application.
He said: “We had some good energy and pressed really well in the first-half – we were magnificent in the first quarter but then got punished with a bit of bad luck that brought them level.
"But the energy, endeavour and willingness was through the roof, probably the best we’ve seen this season.
"We built up some good momentum but that wasn’t stopped by South Shields, it was stopped by other people involved in the game with fouls missed or given, and I think we should be playing against fewer than 11 men for a good part of the game, and maybe even fewer than ten.
"The officials have a tough job but we perhaps needed a bit more help.”