Villa were down 2-1 but got a huge break when John Stones was shown a red-card on the stroke of half-time.
But their advantage was gone when Cash was sent off for a needless late challenge on Phil Foden.
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."