Adam scored a stunning second after a hitting a disputed first goal and said that he will be claiming the opener, but stresses that the most important aspect of the game was the victory against the champions.
He told Sky Sports News: "Of course, [I'm claiming it], it's one of them if you hit the target and get a bit of luck like [we did] as it hit Michael Carrick's leg.
"It was a massive three points, though. We nullified them in the conditions that weren't ideal but we were excellent and it was a massive win."
There was no disputing Adam's second goal as the former Liverpool midfielder hammered in from outside the box.
"It was laid back to me and it sat up for me and I managed to put it in the back of the net and I'll be trying to get more like that."
Stoke are now 11th in the league table.