The Latics could not repeat their FA Cup heroics against Liverpool last weekend despite going ahead through a debut goal from Lee Barnard.
Walsall equalised with a James Baxendale cross-shot five minutes from half-time and Jamie Paterson scored twice after the break to stretch Oldham's poor run to one league win in nine.
Asked what effect the result would have on his immediate future, Dickov said: "Who knows?
"As a manager defeats put you under pressure, but I shall roll up my sleeves and do everything I can to get out of this mess.
"I am gutted because I desperately wanted to get a result. We were hoping it would a turning point after beating Liverpool and that was not because we had better players, but because we wanted it more.
"I thought we should have had two penalties when we were 1-0 in front. I have asked the referee why he didn't give them, and he said they were not penalties. If we had gone two up it would have been a different game.
"But we didn't lose the game through penalties, although that was a massive moment in the game. We started the game so well and got our noses in front, but three or four performances were not up to scratch.
"We saw a lot passion and desire last week but didn't get it from everybody here. Three or four performances were not up to scratch.
"It wasn't lack of effort, it was about doing the right things and getting the basics right. We are in a right battle and scrap now and we have to stand up and be counted."