Four-time world champion Max Verstappen has won twice since Mekies arrived six races ago and has been on the podium in the last four races, finishing second in Singapore last weekend.
Before Zandvoort, a home race where he finished second, Verstappen had not been on the podium for four races.
"It's still zero, guys. It's still zero," Mekies told reporters in Singapore when asked how much credit he felt he could take for the turnaround.
"The improvement in performance is very basically due to the work of everyone trying to analyse the limitations of the car, race after race.
"What is stopping us from exploiting the potential of the car? How can we add performance to the car? Where do we need to add performance for it to convert into lap time?"
Verstappen has gone from being 104 points behind McLaren's championship leader Oscar Piastri after the Dutch Grand Prix at the end of August to 63 adrift of the Australian following Sunday's race.
With six grands prix and three Saturday sprint races remaining, Verstappen is still in the title reckoning although very much a long shot.
"I think Laurent is probably being too nice," the champion said of Mekies' words, with Red Bull consultant Helmut Marko earlier saying the boss was 'too humble'.
"At the end of the day, what is very good is that we just approach it as a proper team effort. We always tried to look into the details. We tried to understand what our weaknesses were. And since a few races it's definitely picked up a lot.
"I do think that now we understand why or how we can be better. By asking the right questions, including Laurent being involved in that, it's just working well."
McLaren retained their constructors' title in Singapore and are expected to do the double and end Verstappen's run of four successive drivers' crowns.