"It's a good feeling and brilliant to get a clean sheet," Chalobah told chelseafc.com.
"A clean sheet and a win we did it together today. The boys knew how massive this game was and obviously, the season has been up and down for us, the consistency hasn't been there, but today was the perfect day to show it against our rivals and the boys were really ready for it.
"We knew it would be a tough game, but I felt the boys were really ready and that's the levels we need to be showing every single game."
On his goal, he continued: "It was something that we were working at during training and we figured out where the danger could be. We worked on it over the last few days.
"I think it's very important that we do our job in our box in terms of clearing it, but we need to contribute in the other box as well."
Chalobah added: "Everyone knows that this season there have been a lot of changes, a lot of new players, but we're slowly starting to see the ability which we all knew we had at the beginning, but things take time.
"The belief was there and the confidence is growing. We just need to keep putting performances in like this and this is the level we know we can get to. We need to show it every single game.
"Now we have four massive games coming up. We're ready and trying to reach our goals."