A late header by Jonathan Forte rescued a point for Crawley, who twice trailed through goals from Febian Brandy and Ashley Hemmings.
Crawley finished with 10 men for the second successive home game with defender Joe Walsh receiving a straight red card for a challenge on Brandy, and Barker acknowledged that plucky Walsall pushed his men all the way.
Smith, who drove behind the team coach, said: "I wanted to play it safe after going sick at home on Thursday night and into Friday, but I was able to go into the dressing-room as it was a 24-hour thing.
"From start to finish we were excellent and I can't fault my side for work-rate on a lively pitch. We took it to them and are disappointed not to get the three points we felt we deserved."
He added: "I was delighted at the way we took the game to Crawley. We are on a run at the moment, but stuck to a gameplan, created a number of chances and played well."