Hamilton, who is leaving for Mercedes at the end of the season, was beaten by Button in Sunday's Japanese Grand Prix.
The two drivers, both world champions, have seemed to get on well at McLaren where their relationship has been presented as generally harmonious.
Hamilton, who has taken enthusiastically to Twitter, caused a controversy at the Belgian Grand Prix last month when he sent out confidential qualifying data to nearly a million of his followers.
Button said at the time he was 'disappointed' by his actions.
"Just noticed @jensonbutton unfollowed, thats a shame. After 3 years as teammates, I thought we respected one another but clearly he doesn't," Hamilton said on his Twitter feed on Monday.
"Funny thing is, we are STILL teammates! All good tho, I plan on giving this team & fans all I got til I cross the finish line in brazil!!!," added the 27-year-old, referring to next month's season-ender.
The messages were soon followed by another retracting what he had said to an audience of followers that now numbers 1.1 million.
"My bad, just found out Jenson never followed me. Don't blame him! Need to be on Twitter more," he explained.
Hamilton is being replaced at McLaren by Mexican driver Sergio Perez next season.
The Briton left Suzuka accusing his Sauber rival, who spun out, of 'crazy' driving in trying to overtake him around the outside at the hairpin in Sunday's race.