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.
He said: "The character we showed was the most pleasing part of the game, especially as we finished with 10 men. After 18 games we are still in the play-off places and this shows we are not a million miles away. We'll keep progressing.
"I felt our best spells were immediately after we conceded and this is a bit of a worry as against better sides we could have found ourselves 2-0 or 3-0 down."
Barker added: "When you're a top-six side you get treated with respect. Walsall are a decent side, they may have gone 12 games without a win, but they are certainly not a poor team."