The Black Cats are already one game behind after their fixture with Reading was postponed due to a waterlogged pitch and have posted three consecutive draws since.
And the Northern Irishman insists that the Mackems must keep up with the teams ahead of them if they are to improve on last season's 13th-placed finish.
|16/1||Sunderland are 16/1 with PaddyPower to beat West Ham 2-1
O'Neill told Sky Sports: "It is important to win games in the Premier league because if you start falling behind it's a long road back.
"We've got three points in the first three games and all three matches have presented difficulties.
"Away at Arsenal it was a tough opening day of the season to get something out of there, especially considering how they are playing now, Swansea were flying very high at that time and Liverpool are a tough game either home or away.
"It would be nice to win a game but we will do that in due course.
"It's too early to talk about catch-up but we're a game behind at the moment, and until we play that game we are always going to be behind.
"I would say after 15 or 16 games, if you have played 16 matches and some have played 17 in the scheme of things it doesn't seem that important.
"At this stage of the season, just getting those early points on the board do mean a lot to clubs so just having that fixture behind means you feel like you're catching up."