Crystal Palace manager Warnock witnessed his side blow a two-goal half-time lead at The Hawthorns, as West Brom fought back to clinch a 2-2 draw in the Premier League.
Victor Anichebe made the difference off the substitutes bench, scoring West Brom's first before winning a penalty for Saido Berahino to equalise in injury time.
However, Warnock was furious that West Brom's first was allowed to stand as centre-back Dawson appeared to catch Palace goalkeeper Speroni with an elbow - which ultimately forced the Argentinian off.
"Unfortunately the referee's not got technology, but it's almost an assault on him [Speroni]," he said.
"He [Dawson] comes from two or three yards away and smashed him in the face, and I don't understand why at least one of the officials can't see that."
Palace went into half-time 2-0 ahead thanks to Brede Hangeland's close-range effort and a penalty from captain Mile Jedinak.
But Warnock believes his team should have had the chance for a second before going 2-0 in front, when Wilfried Zaha was tripped by Dawson in the penalty area with the score still at 1-0.
"He [Clattenburg] had a good game and I wish we had him every week," he added. "But there were two or three decisions that went against us and that cost us. It was a certain penalty in the first half [for Zaha].
"I was told we didn't appeal. But what do they want for us to surround the referee like Chelsea did last week? We shouldn't have to do that really."
