The lead was soon regained through Neil MacKenzie's free kick but Saddlers winger Paul Devlin was then sent off, handing the momentum of the game to Mick Halsall's men.
A defensive error was latched upon by young striker Andrew Barrowman and he handed Walsall a share of the spoils with a well-taken strike.
"I'm disappointed because I thought we were controlling the game as a whole enough to win it," said United manager Laws.
"When the referee sends a player off it sometimes causes more problems for the other team because the 10 men rally and gamble when they have nothing to lose.
"Then one lump up the pitch costs us two points, but we now have two home games and must take advantage of them."
Walsall caretaker boss Halsall was delighted with a point in his first game in charge, but also felt his side could have won.
"I thought we could have won it in the end," he said.
"I was disappointed with Paul Devlin getting sent off because he was having a smashing game and if he had stayed on it would have given us a better chance of winning."