The reigning Guinness PRO14 and European champions Leinster produced a clinical nine-try show to run up a convincing 59-10 win at Rodney Parade.
Experienced hooker Hibbard pulled no punches after the game and admitted the squad needed to pull together ahead of two difficult European away trips.
“We let ourselves down out there,” said Hibbard. “We had the worst possible start and it wasn’t down to them, they are a good team and we know that Leinster are clinical, but we gave them possession and a hell of a start.
“I honestly can’t put my finger on it, I thought that we lacked physicality out there, and cohesion.
“From last week against Edinburgh it was chalk and cheese. Last week we really put it out there but this week we didn’t have it.
“It is tough and you just have to keep the team going and keep their heads up. There are lessons to be learnt from that.”
Dragons now turn their attention to Europe and Hibbard knows the size of the tests ahead.
“The challenge doesn’t get much bigger than Northampton and Clermont, but I think that’s great and it’s straight back on the horse,” said Hibbard.
“It’s exactly what the boys need – when you get a drumming like that at home it hurts your pride, and if it doesn’t hurt your pride then you shouldn’t be on the park.
“There is no better chance than going out to Northampton at their place to show some heart and pride.
“We’ve got to pull ourselves together and dust ourselves off, because that wasn’t us. It does hurt.”