The midfielder made his first appearance for more than five months in Wednesday’s Carabao Cup defeat at Chelsea but lasted just 42 minutes before being forced off with a hamstring problem.
It has since been confirmed the Frenchman, absent since April due to a knee injury, will be sidelined for around a month.
Sanson has endured a hugely frustrating time since joining Villa in a £14million move from Marseille in January, having so far been limited to just 10 appearances, with only four of those starts.
But Smith will not allow the 27-year-old to get downhearted as he faces a further wait to make his mark.
“When he arrived at the club we were doing well so it was always going to be tough. Then he had a knee injury,” said Smith.
“When you miss pre-season it is difficult and he has had to work extremely hard.
“It got to a stage where we got him back in the team on Wednesday and he was playing really well against some very good opponents.
“It is frustrating for him that he felt a twinge in his hamstring and he was frustrated straight away.
“But I saw him on Thursday morning and he was back full of life again, realising it is not a substantial injury and just a twinge. Hopefully he will be back soon.”
Smith, meanwhile, insisted Ashley Young and Marvelous Nakamba have nothing to apologise for after both missed penalties as Villa went down to a 4-3 shoot-out defeat at Stamford Bridge.
Young hit the bar while Nakamba saw his effort saved by Chelsea keeper Kepa after the tie had finished 1-1 after 90 minutes.
Nakamba later posted a message on social media claiming he had “let down” his team-mates, coaching staff and fans.
“They are part of a team and anyone can miss a penalty. It is part and parcel of the game.
“We had our list of takers all the way from one to 10. We told the players that and they were comfortable with it.
“We practiced them for the two days before the game and those were the best takers we saw going into the game.
“There was a process there and unfortunately Kepa has gone the right way for Marvelous.”
Smith was full of praise for 20-year-old Cameron Archer, who scored his fourth Villa goal in only his second senior start.
Archer has forced his way into the first-team squad after impressing in pre-season.
Smith said: “Cameron was given an opportunity to come and train with us and show what he is about. He took the opportunity with that training performance and he has got minutes in games.
“He scored a hat-trick in the first round and then scored against the Champions League winners.
“It was great for him but also the likes of Carney Chukwuemeka and Jaden Philogene-Bidace getting minutes on the pitch.
“Questions were asked about the strength of our bench at Chelsea but Ezri Konsa has come onto the pitch, as have Jaden and Carney. They were players who were coming on against Tottenham and Chelsea at the end of last season and not too many questions were asked. We believe in these players.”