A dramatic last-minute try from full-back Cameron Phelps gave the Vikings a morale-boosting win as they look to avoid the wooden spoon this season.
Betts said: "The target was not to finish bottom of the table and that's what we are pushing toward. Nobody gave us a hope and I know I have said it many times but the fact is some didn't give us a hope of winning a game let alone beating sides that are stretching themselves extensively in the salary cap they are that far away from us."
He added: "We are heading in the right direction and there is a hell of a lot of work going on 24/7, seven days a week to make this club stronger in the right way."
Widnes led from the third minute of the game after a three-try opening salvo in the first 11 minutes, but fell behind for the first time in the match at 22-20 with just five minutes remaining.
But in the dying seconds Rhys Hanbury's kick hit the post and Phelps dived on the loose ball for the match winning try to which Patrick Ah Van added the conversion to seal a memorable win.
Betts was especially impressed with his side's defensive work.
He added: "That was a really good win and I think we were good value for it. Even when they went ahead I don't thing it depicted the game. It was probably our most aggressive win in how we went about it which I enjoyed. The most satisfying thing today was our defence only having just over 20 points scored against us."
Huddersfield coach Nathan Brown said his side needed to play with more discipline and control after their third defeat in a row.
Brown said: "I thought we actually hung in there well for most of the game. They scored their last three tries from kicks and it wasn't if our effort wasn't there and it wasn't like we went out there and didn't try."