Germany were shocked in their World Cup Group E opener as they were beaten 2-1 by Japan last week, but kept their knockout stage hopes alive with a hard-fought 1-1 draw against Spain on Sunday.
Kimmich was pleased with Germany's improved performance and reckons they may just as easily have sneaked in a winning goal after creating better chances.
"Fortunately, we were able to come away with a point," said Kimmich, as quoted by the official DFB website.
"It felt like Spain had more of the ball, and we knew that we'd have to do a lot of running today.
"I feel like we had the better chances though. We had more clear-cut opportunities and, with a bit of luck, we could have got the win.
"A draw is a fair result though. It was certainly a step up from us.
"We won the ball in some promising positions that perhaps could have led to more as well."
His team-mate Leon Goretzka echoed his sentiments on the game, and added that a lot of hard work went into the draw against Spain.
"It was a real battling performance, and that's the way you have to do it at a World Cup," said Goretzka.
"Fulle's goal is just determination personified. We worked incredibly hard today, and I think you can see that in the build-up to the goal."