The game was balanced on a knife edge after an hour, with the scores locked at 4-4, but tilted dramatically Saints' way when Betts' men were reduced to 11 men. Saints took full advantage to run away with the game, tries from Lee Gaskell and Francis Meli securing a 16th successive derby victory and giving Nathan Brown his first success as coach.
"I thought there were two good teams out there," Betts said. "I thought we had a chance of winning the game. It was one of those tough days to be really skilful but I thought we had the better opportunities. It was only when we were down to 11 men that they really got some opportunities to score tries and they did."
Betts added: "I'm really proud of my team. I thought we played better this week than we did last week. When it turns into 11 versus 13 it becomes very tough. We defended really well with 11 blokes actually."
Widnes, who took the lead through Stefan Marsh's early try, gave a debut to England forward Gareth Hock, who has joined them on loan from Wigan.
"For his first game he looked pretty solid at times, so he'll only get better," Betts said.
St Helens coach Brown was delighted with his side's response to their humiliating 40-6 home defeat by Huddersfield and did not believe the flurry of cards was decisive.
"I was confident because our defence was so good," Brown said. "I didn't think they looked like scoring. I thought we were on top at that stage. It's good to get a win. I was happy with our effort and our defence. Our defence was far, far better than last week.
"I thought the opposition ripped in. They played really well and, if we had the same commitment as last week, we would have got beat, without a shadow of doubt."
St Helens went into the game without England hooker James Roby, who has a minor foot injury, and lost prop Josh Perry with a worrying knee problem after only five minutes. They suffered further disruption caused by injuries to Jonny Lomax and Lance Hohaia.