The Black Cats had a numerical advantage for an hour after Canaries goalkeeper Mark Bunn was sent off in the first half, but they could only pick up a point as Craig Gardner's penalty cancelled out Wes Hoolahan's opener.
The result extended Sunderland's winless run to seven games and left them just four points above the relegation zone, and O'Neill admits they are struggling to deal with the tough situation.
"The pressure has got to the players," he said in The Sun.
"When you are on the run we are at the moment then confidence is a wee bit low. We should have made the extra man count - it is frustrating."
Sunderland entertain Manchester United in their first game after the international break and then face Chelsea, Newcastle and Everton at the start of a difficult run-in.
O'Neill added: "I wouldn't stop at the next four - they're all tough games but the whole league's been tough for us.
"My worry is we have players on international duty and won't see them for some time. I hope they come back in one piece."