After a sizzling opening 13 minutes which saw City take a two goal lead, through Raheem Sterling and Gabriel Jesus, Napoli clawed their way back into the game despite seeing a first-half spot kick superbly saved by Ederson.
"I thought the lads showed good character out there. Ederson has kept us in it and we need to say a big thanks to him," said England international Walker.
"We always knew they would come at us in the second half, with us going 2-0 up," he added.
City manager Pep Guardiola, who had praised Napoli highly before the game, said the win had come against high class opposition.
"Napoli are an exceptional side so I was expecting them to play the way they did," he said.
"They are one of the best sides I have faced as a coach so I am so, so happy to have won this game.
"They are one of the best teams I think in Europe. Today we beat an incredible team and we had to give an incredible performance to do that so I am very happy," he said.
(Reporting by Simon Evans; Editing by Toby Davis)
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