The visitors led 14-12 at half-time, after tries from Catalan pair Thomas Bosc and Steve Menzies were countered by two from Patrick Ah Van and one from Dave Allen. But the action was all one way after the interval, with Louis Anderson, Oliver Elima, Damien Blanch, William Barthau, Mathias Pala and Zeb Taia all dotting down for the Dragons.
Betts said: "I thought we failed to match them physically in the second half. I feel like Brian Clough but it was a game of two halves. When we came out in the second half, they scored first and then we just couldn't get ourselves back into the game."
He added: "They just seemed to roll over the top of us and that gave [Eloi] Pelissier the opportunity to kill us around the ruck.
"His speed and his directness on the back of the physicality of their forwards was too hard for us to handle and we just couldn't catch our breath.
"We stopped bending our backs in defence, tried to take a couple of short cuts to try to slow them down with hands in the ruck and the ball came out and the referee penalised us.
"That's what happens when you're going backwards like we were, we were just absorbing the game and giving penalties away because we couldn't get back."
Relieved Catalan coach Laurent Frayssinous was delighted by the way his side fought back from 10-0 down and the way they bounced back from their defeat at Wigan last weekend.
Frayssinous said: "I was very pleased with our second-half performance, the players stuck to the game plan and knew what their strengths are and played to them.
"We have a very good team when we do that. We don't want to take short cuts and that's what we did last week and in the first half. We respected the ball and did the hard work in the second half and it showed on the scoreboard."