The Saddlers extend their unbeaten run to nine games with a 2-2 draw just as Crawley thought they had pulled off a shock win at the Banks's Stadium.
Smith said: "It says a lot for my team that they scored twice so late in the game and then went looking for the winner."
Crawley were seeing out time when the Saddlers pulled a goal back with a deflected shot from Jamie Paterson, who had earlier hit a post, in the 89th minute.
Then Will Grigg notched his 19th of the season from Andy Taylor's low cross in the third minute of stoppage time.
Crawley built a two-goal lead through Jamie Proctor and Paul Hayes but have now drawn their last four matches.
Smith admitted the heavy Walsall pitch meant there were some tired legs in his team after Tuesday's win over Tranmere.
He added: "When Jamie hit the post in the second half I thought it was going to be one of those days. But it was a really good comeback.
"The first half was a bit lacklustre, but we had the best chances and I thought we should have had a penalty for a foul on Will Grigg. It was probably a fair result, but I don't think we deserved to be two down.
"We showed another side to our game and deserved at least a point."