West Ham had an early lead through Lucas Paqueta before Villa struck in the second-half through Amadou Onana and Rogers.
"To go one-nil down is not what we want but it’s about how we react, how we show our determination and courage within us to come back in the game,” said Rogers.
“Thankfully we got the win and I thought we played pretty well.
“We controlled the game and when you keep pushing and keep pushing, you hope it goes in. And luckily it did.”
Asked what changed in the second half, Rogers replied: “A bit of belief, a bit more patience, a bit more forward thinking – I think we had a lot of the ball in the first half, but probably not risking enough or trying to go forward and make that difficult pass.
“In the second half we did. I know we didn’t always get it right, but we create more chances, create more mayhem in our attacking third and that’s where our goals came from.
“So, we’re just happy we won.”