The Black Cats were undone by a late Robin van Persie free-kick at the Emirates Stadium after one from former Gunner Sebastian Larsson had cancelled out the Dutchman's first-minute opener.
It made for an ultimately disappointing afternoon for the Wearsiders, but Vaughan is taking encouragement from their performance ahead of Saturday's trip to Bolton.
"We had the chances to get ourselves in front and in a different game we might have, but it wasn't to be," Vaughan told www.safc.com.
"The keeper made a great save and we possibly could have done a bit better on other occasions. Now it's down to us to get a good result this weekend.
"We asked questions of them and on the whole the lads were positive after the game that we played well. Yes, we could have done better, but it's something we can build on."