Russell's comments come at a turbulent time in the relationship between the drivers and the FIA.
Since the last race in Brazil, the GPDA put out an open letter asking the FIA to treat them "like adults", after a controversy over drivers swearing in news conferences.
The letter also made a reference to a lack of transparency over how money for fines for driving transgressions was being used.
Wittich's departure followed a few days later, and shortly after that it emerged that the FIA compliance officer Paolo Basarri had also been sacked.
Russell said: "Talking as a fellow driver as opposed to my role with the GPDA, everybody felt with certain things that have happened that we wanted to stand united.
"At the end of the day we just want to be transparent with the FIA and have this dialogue.
"And the departure of Niels is a prime example of not being part of these conversations. (The letter) is kind of us putting the pressure back on them."
Russell admitted that the drivers were not fully content with some aspects of Wittich's work since he became race director at the start of the 2022 season. The German has been replaced by ex-Formula 2 and Formula 3 race director Rui Marques for the final three races of the season, starting in Las Vegas this weekend.
He said: "There is no secret that some were not happy with what was going on in terms of the decisions that were being made, but he worked together with us and we could have helped improve the matter.
"Sometimes just hiring and firing is not the solution. Let's see what this new era brings, but every time you make a change you have to make one step back before you take two steps forward."
McLaren driver Lando Norris said: "I don't know what's going on there. Obviously things are not running as smoothly as we would want."
Haas driver Kevin Magnussen echoed Russell’s comments, saying that the drivers felt ignored compared with the days of the former FIA F1 director Charlie Whiting, who died on the eve of the 2019 season.
"I compare with the Charlie Whiting days," Magnussen said. "He was someone we felt really connected to and we were really being listened to, but now we feel it’s more us against them and it should be a closer connection. We can help a lot."