With Villa trailing 2-1 but with a man advantage after John Stones had seen red for the visitors, Cash evened up the numbers when he picked up two yellow cards in the space of three minutes.
Both were for fouls on Phil Foden, the second when he chopped down the City man after losing the ball.
Smith said: “He will be down, especially with the earful he got off me in the dressing room after.
“He will learn. He is a young lad in his first Premier League season and I think he will be a super player. But he was reckless and stupid. We won’t have many better chances of going and beating a team like Manchester City.”
Villa got the perfect start when John McGinn fired them in front after just 20 seconds before City went on to dominate the first half, going in front through goals from Foden and Rodri.
But Stones’ dismissal, for a rash challenge on Jacob Ramsey, offered Villa hope before Cash was also dismissed and the visitors ran out comfortable winners 10v10. Victory left Pep Guardiola's men eight points from claiming the title.
Smith continued: “I am a bit frustrated. It was a great start to the game. We talked about playing balls in behind their full-backs .
“For me we have the best runner in the Premier League in Ollie Watkins and he set up John McGinn for the goal.
“But then to be fair I was stood in awe for 20 to 25 minutes of wonderful passing and moving from Manchester City.
“The two goals are what frustrated me because we didn’t deal with those well. We know their goalkeeper can play 70 yard balls, while the second was from a second phase corner kick.
“If they are cutting you open with one touch movement and scoring excellent goals it is easier to stomach.
“Them going down to 10 men gave us a great opportunity but then we get a red card as well with a stupid and reckless second yellow.”
Stones was dismissed after referee Peter Bankes consulted his pitchside monitor and overturned his original decision of a yellow card.
Smith said: “I thought he was unlucky. He has timed his challenge late but I never felt our player was in danger.”