Dick Advocaat praised his players for summoning up the spirit of their successful fight against relegation to open their account for the new Premier League season.
The Black Cats fought back after going behind to clinch a draw with Swansea at the Stadium of Light to remind the Dutchman of the resilience they showed during his nine-game rescue mission at the end of the last campaign.
"It's a much better feeling this time, 1-1 against a very good side," said Advocaat. "Swansea are a good team with good players, but the way we played with the spirit we showed last year, you can see that you will get results.
"With a little bit of luck, if the referee had given us the penalty that was a penalty, we could even have won. But I can live with 1-1, to be fair to Swansea as well."
Swansea took the lead somewhat against the run of play in first-half injury-time when Kyle Naughton picked out Bafetimbi Gomis's run into the box and he finished clinically with a first-time strike.
However, Jermain Defoe was similarly lethal when presented with the chance to level from Jeremain Lens's 62nd-minute pass, although it took a series of fine saves by Costel Pantilimon to secure a point.
Sunderland thought they should have been awarded a 66th-minute penalty after Jack Rodwell's shot appeared to come off defender Ashley Williams's arm, but referee Neil Swarbrick was unmoved, much to Advocaat's astonishment.
Asked if it was a penalty, he said: "Yes, 100 per cent - at least the way they are now giving penalties, it was a penalty. I could see it on television and it is clearly against his hand."