The Black Cats lost to the Gunners by one goal to nil but spent the second half throwing everything they had at the Arsenal goal.
Try as they did, though, Sunderland could not get back on level terms but O'Neill believes if they continue to perform like they did then the fans will continue to back them to the hilt.
O'Neill said: "That type of performance is what we should be all about.
"In our last three home games we've been brilliant against West Ham and Arsenal, and a bit of a mish-mash against Swansea, but what we want is a performance up near that mark we've shown in two of those three games.
"In terms of intensity it is very difficult to keep that up for a full 90 minutes, but we did well, and that's why the crowd stayed with us to the end.
"Obviously it was Arsenal, and there was a great crowd in, but they will stay with you, keep coming along, if that's the type of intensity and effort you want to put in."
Sunderland last week