City now sit on the brink of the knockout stages, but they were thankful to Ederson for a penalty save from Dries Mertens after Pep Guardiola's men had raced into a two-goal lead.
Although the Premier League leaders dominated the first half, they were ultimately made to hold on for three points after Amadou Diawara converted Napoli's second spot-kick chance and the Italians then pushed for an equaliser.
While Walker and his team-mates had expected the onslaught, he still felt the need to thank Ederson for his contribution as the keeper delivered an all-action display.
"We always knew they would come at us in the second half, with us going 2-0 up," Walker told BT Sport.
"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."
Despite a nervy second half, John Stones was pleased with the way City played against a side who sit top of Serie A with a perfect record after eight games.
"There were a lot of runners in behind," the defender added. "We knew they had great, patient football, a lot of one-touch passing, setting the ball, a great attacking threat.
"They've played a lot of great teams in the Champions League and won. We knew it was going to be a tough test, them coming here.
"We wanted to play our game and some of the football was great to watch. We're upset to concede the goal that we did. I thought it was a bit soft. But it was a great team performance."
City require just one point in the return fixture to seal their progression to the last 16 and Stones added: "We've put ourselves in a good position with a lot of games to play still.
"We've got to keep going, game by game. This was a great test to see where we're at after a good run of hard games."