A fluke Tom Williams goal had the Saddlers on course for three points but Jason Lowe levelled in spectacular style from outside the box just two minutes from time.
Oldham had a goal disallowed, a penalty appeal turned down and finished the game with 10 men after Filipe Morais was shown a straight red card for his tackle from behind on Jordan Cook.
Dickov said: "Nobody in the ground knows why he gave a free-kick which led to Walsall's goal and nobody understands why our early goal was disallowed.
"We should have had a clear penalty and the sending-off was just wrong - I even asked their player if he thought it was a red card and he couldn't believe the referee's decision.
"Overall it was a scrappy game. We were nowhere near our best but I always felt we could get back into it. It takes a lot of character to come back with 10 men but they kept on having a go and they got their reward."
Source: PA
Source: PA