Hughton went into the contest with his team having won one, drawn one and lost three of their opening five top-flight games this term and reports suggesting he could be facing the sack if they were beaten at the Britannia Stadium.
Norwich went on to claim a 1-0 victory, moving them up from 17th to 14th in the table.
And afterwards Hughton - who guided the club to 11th last season in his first campaign in charge, and then had his squad bolstered by a considerable spending spree over the summer - admitted he had been under more pressure than usual in the build-up to the fixture due to his side's league position.
Pilkington, meanwhile, made it clear what he thought about the speculation the axe could have been hovering over Hughton.
"It's crazy," the 25-year-old Republic of Ireland international told Press Association Sport.
"I wrote on Twitter asking if it was too early for Paolo Di Canio (the former Sunderland manager, who was sacked on September 22) to go, given we're only five or six games into the season.
"We have brought a lot of new players in and it takes time for them to gel. But you have seen (at Stoke) what we can do."
The lively Pilkington provided the assist for the 34th-minute goal that secured all three points for Norwich, teeing up Jonny Howson, who fired in from outside the box as the Canaries took advantage of sloppy play from their opponents.
The visitors had already hit the bar through Ryan Bennett and were good value for their lead.
They survived a scare after the break when no penalty was given despite Leroy Fer pulling back Kenwyne Jones in the box - the Norwich man later admitted he had done so - but subsequently came close to scoring again, with it requiring a great save from Asmir Begovic to keep out Robert Snodgrass' curling shot.
Pilkington felt Norwich could have triumphed by a greater margin, but emphasised the sheer fact that a win - and an away one at that, only the club's second in the league in 2013 - had been achieved was the most important thing.
He was also delighted with his own role in it, having made his first Premier League start of the season.
"I thought we could have had more goals," he said.
"We had a gameplan where we wanted to press high and get in their faces, win the ball up high and create chances from there, and I think we did that.
"But it's all about winning games at this level and picking up the three points, especially away from home. It is a massive win for us.
"I've not been in the team recently. I've had to wait for my chance. I had a few niggles in pre-season but I'm over that now, and hopefully I can keep my place."
Stoke boss Mark Hughes, whose side are now 15th, also on seven points from six games, was disappointed by the Potters' showing.
"You've got to be brave in possession and brave out of possession and on occasions we weren't," Hughes said.
"Many teams will try to close us down and stop us playing. If that happens you have to do other things and recognise when the momentum of the game changes and things settle down again - then you can start to play your football again.
"Unfortunately, we didn't get that understanding quick enough and continued to do things that encouraged Norwich more than us.
"We never really got any momentum or a head of steam to really ask enough questions of Norwich for a sustained period."