Attacking midfielder Grealish has missed Villa's last seven matches due to a shin complaint, with Smith's side winning only two of those games.
The Villa captain will now sit out the clash with Liverpool at Anfield this weekend and is likely to remain a doubt for when they next play, against Manchester City on April 21.
"Myself and Jack were quite optimistic to get him back a bit sooner than he probably should and he's had a setback that will probably put him back a couple of weeks," Smith said.
"We know it's not a long-term injury and he will be back. We all, Jack included, probably pushed him back a little bit too quickly. We wanted him to get back and he had a little setback."