When substitute Yoann Arquin headed in Alan Sheehan's free-kick the Magpies thought they had stoles all three points, only to be denied by a flagging referee's assistant.
Smith felt the decision was correct but visiting boss Chris Kiwomya disagreed.
Smith said: "We work on free-kicks, holding the line, and he started in an offside position. He was standing offside."
But a very disappointed Kiwomya, who spent 20 minutes with referee Iain Williamson after the game, argued: "I just thought it was too close to call and it had to be a goal. I have looked at it a couple of times (on video) and I couldn't see it was offside, but you have to accept these decisions. We didn't get enough (today)."
Walsall, who had won three games on the trot, took the lead five minutes into the second half when former West Brom striker Romaine Sawyers, making his full debut, burst forward and smashed a right-foot shot inside the right-hand post.
The Saddlers had chances to make sure of all three points but former County striker Craig Westcarr and Sam Mantom failed to beat goalkeeper Bartosz Bialkowski, who also made a superb 90th-minute save from Malvind Benning.
The Magpies equalised after 73 minutes, Arquin cleverly heading in a far-post cross from Sheehan, while Walsall keeper Richard O'Donnell - named man of the match - pulled off three outstanding saves during the game.
Smith said: "We could have been out of sight if we had taken our chances but we lost our way in the last 15 minutes. Our lads were aggrieved at half time because Dean Leacock (the County skipper) could have had four yellow cards.
"My lads know they can be better on the ball and we didn't pass the ball as quickly as I would like, but the pitch was slow.