The right-back helped the Blues to a hard-fought 2-1 victory at Old Trafford to extend City’s lead atop the Premier League table to a staggering 11 points.
“It’s a massive win,” he told CityTV. “It’s a big three points, especially over local rivals.
“To get one over on them on their turf is fantastic.
“[My first competitive Manchester derby] was good. It’s always good when you’re winning!
“I’m buzzing. I’m trying to hold it in! I want to scream or something!”
City were dealt a suckerpunch when United equalised within minutes of Silva’s strike – on the brink of half-time.
Walker asserted his side were unaffected though and revealed the half-time teamtalk was a positive one.
“Pep Guardiola told us to keep going,” he added. “He wasn’t unhappy or disappointed.
“We shouldn’t be. We had more possession. We were done on the long ball.
“It was a great finish from Marcus Rashford but we had more of the ball and controlled the game a lot better. We just needed to take that into the second half.”
City goalkeeper Ederson produced a terrific double-stop to deny Romelu Lukaku and then Juan Mata from close range late in the game.
Walker hailed his shot-stopper and tipped him to become a great.
“He is fantastic,” he continued. “Eddy is a top-class ‘keeper.
“He proves it day in, day out at training and he proved it on the big stage.
“He’s right up there. I’ve played with some good goalkeepers – Hugo Lloris for example and David De Gea is world-class as well.
“Eddy is young and has potential. He wants to learn each and every day. He’ll go right to the top.”
With City having claimed such a substantial lead in the Premier League title race, many have dubbed the Blues champions elect.
However, Walker has warned against complacency.
“You sound more confident than me!” he joked to CityTV. “We have to keep our feet on the floor and keep working hard, preparing physically and mentally.
“We have another important one on Wednesday against Swansea. We have to keep getting three points.”