But Villa then staged an improbable fightback, with Tyrone Mings and Tammy Abraham netting in the 82nd and 86th minutes, before Andre Green headed the equaliser deep into stoppage time. We pushed a decent team, with a decent manager and assistant with a lot of experience, back.
"What it does prove is that we have a lot of fighting spirit in the dressing room".
Smith admitted Villa, who moved to within three points of the play-offs, must improve their mentality if they want to achieve their play-off goal.
Sheffield United striker Billy Sharp scored a hugely controversial goal against Aston Villa on Friday night as it appeared he kicked the ball out of Lovre Kalinic's hands. I think he [Kalinic] will be disappointed with himself for going to ground, but I'd have to agree if that's the rule.
"I thought we started the second half really well and then unfortunately the officials didn't do their job in the 52nd minute".
He said: "I was in love with the game for 82 minutes but then something happened in the final 10 minutes".
The former Sheffield Wednesday defender, whose Villa side remain eighth, said: "Three goals in the last 13 minute was really dramatic but we still have a lot to work on because we can not start games like we started against Sheffield".
"Fair play to Billy Sharp, he hasn't taken the chance and he's got a goal from it".
"We're trying to win the promotion and these are the games when you get in front, you've got to win the game. It took the shine off my hat-trick, I'd have rather have not scored and got the three points to go top".