Betts saluted his 12-man side after they clawed back to snatch a thrilling 22-22 home draw but said afterwards: "It was an atrocious decision and an absolute joke."
The forward, on loan from Wigan, was red-carded on the half hour by Hicks for dissent after Matt Diskin bagged the Bulls third touchdown to stretch their advantage to 16-4.
Betts said: "It was a very poor decision and a player should not be sent off for swearing. Are we in a schoolyard? You shouldn't get sent off for swearing. Maybe warn him or a sin bin but not a sending off. It's very frustrating."
Widnes were 20-4 down at half-time but scored three tries without reply in the second half with a Patrick Ah Van penalty five minutes from time earning a point.
However, Betts was pleased with this team's battling qualities, and he said: "It was an epic second half and a great performance of endeavour and enthusiasm.
"We could not get a grip on the game at first but got stronger and had great self-belief. We fought as hard as we could and even had opportunities to win it."
Bradford coach Francis Cummins said: "You can't play without the ball and we couldn't put any pressure on Widnes in the second half.
"We had a few guys busted and the penalty count was surprising - but no excuses. I cannot fault my players for their effort but it was an awakening after Sunday's good result over Huddersfield."
Cummins also revealed three injury concerns, with Jamie Langley suffering a groin injury and Matty Blythe and Chev Walker sustaining ankle problems.
- Sports & Recreation