Palace controlled large periods of the game at Selhurst Park, but proved unable to find the all-important breakthrough on a tough afternoon.
Yeremy Pino, Daichi Kamada, Jean-Philippe Mateta and debutant Christantus Uche all went close, but Sunderland – and in particular their goalkeeper Robin Roefs – held firm.
Despite the stalemate, Glasner maintained a level perspective following the result.
"There's a little bit more disappointment about the result," admitted Glasner. "But I think, especially at the end, we deserved to win the game.
“But Sunderland had a great goalkeeper today, who made three, four, incredible saves.
"We missed one or two chances, and if we don't score, then it's important not to lose.
"I think we were very consistent defensively today, again. We gave them one chance in the first-half. We saw an exceptional block from Tyrick Mitchell, everything else in the game I think we controlled really well.
"But yes, in terms of scoring goals it was not our best... in terms of efficiency it was not our best performance. And then it's a draw, but we're still unbeaten. It feels a little bit like it could have been more, but it's all good."
