Hamilton has called for a better platform to give drivers for their anti-racism gesture following a rushed pre-race kneel in Hungary.
Fourteen of the 20 F1 drivers took a knee ahead of the start of the opening two races of the season in Austria as part of an anti-racism message, showing solidarity with the ongoing activism around the world against racial injustice.
Before Sunday's race in Hungary, the drivers once again wore T-shirts reading 'End Racism', but there was no organised kneel, leading to a fractured show between those who did and did not take a knee.
F1 set a dedicated place in the pre-race schedule to allow drivers to kneel in the season-opening Austrian Grand Prix, but has not done so ahead of the anthem at either of the last two races.
Hamilton also called on F1 to offer a better platform for the drivers to further the message of condemning racism and improving diversity in the sport.
"Moving forwards, we need to speak to Formula 1 as they have got to do a better job," Hamilton said on Sky Sports F1 after the race.
"It was such a rush. I was getting out of the car, running over, quickly taking a knee. They need to do more.
"I don't know why they only did it for the first race on the start. They have not done it since then.
"They have come out to say they are fighting for diversity and to end racism, but they are not giving us the platform to continue that.
"It is all rushed, so I think they need to give us more time. I will be speaking to them, probably send an email over the next couple of days and try to coordinate with them on that.
"Because they do want to, but I guess there was not good enough communication."
Hamilton also revealed that GPDA chairman Romain Grosjean felt there was no need to continue having drivers take a knee, and that it was not raised in the drivers' briefing on Friday.
"He doesn't think it is important to do it," Hamilton said in an interview with Sky Sports F1.
"He is one that thinks we did it once and that is all we need to do.
"So I tried to speak to him about what the problem is, and it isn't going away, so we have to continue to fight for it.
"I think this time he didn't mention anything in the drivers' briefing and neither did Sebastian [Vettel]. Sebastian and I messaged each other and he stressed, as I did, the importance to continue to do it."