Do you mean in it's entire history or from a certain point in a modern era? I mean, the FA Cup started in 1871-72, but the Football League was only formed in 1888, 16 years later.
I thought we ranked something like 18th-20th in terms of clubs with most time in the top flight since the War, so I expect most of the teams who are higher in that table to not have been knocked out by non league opposition, with only a small number of notable exceptions, post war. We've nearly always entered the FA Cup at the 3rd round stage and it's a very rare thing for a non league team to get to the 3rd round let alone the 4th or 5th.
However, in the early years of the FA Cup it probably happened quite a lot, as I know Spurs won the whole competition in 1901 while a non-league club themselves.
Also, we were formed in 1876 and were non-league ourselves until 1899. We must have lost to non league opposition before then as our league record shows 7 losses in 1889-90, 3 in 1890-91, 3 in 1891-92, 6 in 1992-93, 2 in 1893-94, 1 in 1894-95, 4 in 1895-96, 1 in 1896-97, 3 in 1897-98 and 5 in 1898-99. We often only got as far as qualifying rounds in the FA Cup including 1899-00 the year we had entered div 2 for the first time.