Louis Dodds put Vale ahead early on and they looked set for three points until Phil Edwards levelled with a 82nd-minute penalty.
Tommy Fraser put Vale ahead again but they could not hold on and Andrew Procter netted a late second for Stanley.
Adams, who placed his entire squad on the transfer list on Monday, said: "It's disappointing to lose the three points when you get so close. We let nerves get the better of us and you could see that at times.
"I'd certainly like to see the penalty decision again because it looked harsh from where I was standing.
"But we have to stop giving away so many free-kicks and we also keep straying offside. When you do that you inevitably invite pressure.
"It's not all doom and gloom by any means, but we will be looking to strengthen in certain areas and new players will be coming in."