The Black Cats battled for a 0-0 stalemate at Emirates Stadium to make it four Premier League games unbeaten.
Sbragia conceded Arsenal were guilty of spurning the chances they had on goal, but he hailed the dogged nature of his team.
He told Sky Sports: "I am delighted with the point. We said we'd be over the moon if we came here and got a point.
"We said we would try and keep a clean sheet and try and steal a goal. We had a little half-chance late on.
"We rode our luck a bit but we doggedly stayed in there. The defence and the midfield were excellent today. Overall I am really pleased.
"The longer the game went on we thought we probably had a chance, but to be fair they missed a couple of good goalscoring opportunities. We had a little bit of luck on our side."