The Saddlers, who have now drawn against the Black Cats on two consecutive Saturday, fell behind in an otherwise even first-half when Aiden McGeady fired in from six-yards.
But Keates’ side pulled level after the interval when Andy Cook smartly turned in Nicky Devlin’s cross.
From that point, Walsall were the team that looked like going onto win the game with Morgan Ferrier seeing a low drive saved by Jon McLaughlin while Cook headed against the crossbar.
“I think on the second half performance we did well and maybe could have just shaded it and come away with a victory,” Keates said.
“We spoke to them at half-time and just told them to play with a little bit more belief in themselves.
“We were very tentative in the first half, looking almost, not scared to make a mistake, but sometimes you’ve got to play without fear in football and you have to play knowing that you might make a mistake and play without being scared.
“Second half, we said to them go and play like we did at the beginning of the season and we looked a lot more like ourselves.”
Cook’s goal was a special moment for the striker who is a boyhood Newcastle fan.
And Keates was delighted with his performance and the performance of centre-back Connor Johnson who stepped in at the last minute after Russell Martin was ruled out through illness.
“He (Cook) is a Newcastle fan, he’s a Geordie lad and he will take great pleasure in that,” the boss continued.
“He was outstanding. I also thought Connor Johnson was absolutely outstanding today.
“He didn’t know until 1pm that he was in the team.
“We lost Russ Martin through the night to a sickness bug, I spoke to Russ at 10.30am and he was still throwing up, so Connor got dropped in at the deep end and I thought he was absolutely outstanding.”