The England international opened his club account for the season with a vicious, dipping effort from distance to cancel out Rodrigo Bentancur’s opener for the hosts, with Villa then going on to win Sunday’s game thanks to Emi Buendia’s second half strike.
Rogers, named PFA young player of the year in August, has endured a difficult start to the season in Villa colours and was sarcastically cheered by a section of the Villa Park crowd during last month’s win over Bologna.
But Cash believes there was never any doubt the 23-year-old would come good.
“That’s football,” he said. "You see it a lot of times with different players and circumstances over the years.
“In tough moments you need the help and support of the fans and sometimes, at all clubs, you take some criticism.
“That is part of the game. I am delighted for him. He has shown that class is permanent. He needs to keep building and doing it because he is obviously a great player.”
Rogers has experienced a stunning rise since joining Villa from Middlesbrough in January last year for an initial £8million.
The Halesowen-born star scored 14 times in all competitions last season and is an increasingly key part of England boss Thomas Tuchel’s plans.
Asked if Rogers had required an arm round the shoulder during the tough early weeks of the campaign, Cash replied: “I think you do. When you are a young player - and he is still young - who has only had a season and a bit here, it is tough.
“When things go tough, it can affect you. He is a human being. We all are. When things aren’t going well, it ain’t easy.
“Sometimes players read criticism, it is part of life. We are the ones who need to turn it around and perform. So yeah, I am happy for him.”
Cash was involved in Villa’s winning goal after hitting a pass Sky Sports pundit Roy Keane described as the “ball of the season”.
After failing to win any of their first six matches, Unai Emery’s team have now won five matches on the spin in all competitions and will be aiming to maintain their perfect record in the Europa League when they visit Go Ahead Eagles on Thursday.
“We had a tough start to the season but now we are starting to pick it back up again, which is great,” said Cash.
“We didn’t panic. Some of the results we got away from home, at Everton and Sunderland, are now sort of looking good for us.
“On Sunday we were delighted. It was a great win away from home and hopefully we can keep building on it. We’re getting better, five wins in a row, so we are delighted.”