Messi, who hit his 12th career hat-trick against Atletico, has now scored 192 goals for Barca, just four behind Kubala's haul of 196.
And while the Argentinean international is yet to overtake Kubala, he admits he already has Cesar Rodriguez's all-time record of 235 goals in his sights.
"I'm pretty calm about it," Messi said, according to AFP. "I just take it a game at a time, but obviously I'm very excited about becoming top scorer.
"Many years have gone by and it's still the same player [Kubala].
"Hopefully I can beat his stats. I want to continue breaking records here."
Atletico are one of Messi's favourite victims, with the dimunitive forward having scored 14 times against them, including three hat-tricks.
And despite Barca having notched up 22 goals in just five league games so far this season, Messi believes there is stil room for improvement, especially with coach Pep Guardiola experimenting with a new 3-4-3 formation.
"We feel pretty comfortable with it [the new formation].
"There are some things we still aren't doing well, just like with the previous system, but that's okay.
"It takes time and practice. We still aren't totally used to it.
"Personally, I'm pretty happy, because up front we have more space and we can link up better with the midfield players, and receive more passes."
Barcelona's next game will see them take on BATE Borisov in the Champions League on Wednesday, where they will look to build on their opening Group H match against AC Milan, which ended in a 2-2 draw.