Button won the race at Spa but British newspapers on Tuesday reported his dismay at the incident.
"We work so hard to improve the car and keep things like that secret and private. I didn't want to see it on Twitter," said Button, whose relationship with Hamilton has hitherto been unusually harmonious for title rivals.
"It was the whole telemetry from qualifying. It wasn't just the rear wing. I was very surprised and disappointed," said the 2009 world champion, who added that the matter was also now behind him.
"I think it's done now. I don't think it's for me to be angry with Lewis. It's not a personal thing," he said.
Hamilton had tweeted telemetry from his car and Button's to show his nearly a million followers the difference between a new rear wing being used by his teammate and the older one he had opted for in qualifying.
The 2008 champion's tweet was swiftly deleted on team orders but not before it had been widely seen and copied in the paddock.
Teams guard such data with intense secrecy, in a sport with spies watching every garage, and former McLaren driver David Coulthard said in a column in the Daily Telegraph that the incident was "at best embarrassing".
Recalling how in his day there were people who would trawl through rivals' refuse bins on the Monday after a race in search of just such information, the Red Bull consultant said the use of shredders and computer security had made such a leak even more valuable.
"McLaren are playing down the sensitivity of the information but at the very least it has shown their rivals exactly where their lap time was won and lost with their new wing as opposed to the old one," Coulthard said. – Reuters