Smith's father Ron passed away last week as a result of the coronavirus, following a battle with dementia.
Villa are two points from safety with nine games remaining in the season.
"I always used to ask him every day how his dad was getting on," Grealish said.
"Then when the news came it was devastating for him and his family. Us as players have tried to be there for him and try to help him.
"One good thing about football when you are having a problem away off the pitch, when you do come into training or play a match, it takes your mind off everything else. It certainly does for me. That's what we tried to do for the manager.
"I'm sure we all want to avoid relegation even more now, for the Smith family."