Sachs, who was diagnosed with dementia four years ago, was buried in North London on Thursday.
Cleese, 77, tweeted that he was very sad to learn of the death and called Sachs "a very sweet, gentle, and kind man and a truly great farceur".
Sachs' performance on Fawlty Towers was one of the most widely imitated comedy characters from that era, the BBC said.
"The waiter...often said little more than the word 'Que?' to generate laughs, but arguably his most famous line was 'I know nothing'," it said.
After Fawlty Towers, Sachs went on to play Ramsey Clegg on ITV's "Coronation Street" and had a brief role on BBC's "EastEnders".