The result has left City four points behind league leaders Arsenal.
City thought they had made the perfect start when Bernardo Silva fired home from a corner, but the goal was ruled out for offside.
It set the tone for a night where Guardiola's side created plenty but could not find a way past a stubborn Sunderland defence.
Both teams had chances in an open first half. Brian Brobbey and Erling Haaland were denied by saves, while Trai Hume headed over late in the half as Sunderland threatened at the other end.
City increased the pressure after the break, with Savinho twice going close early in the second half.
Sunderland goalkeeper Donnarumma saved from Eliezer Mayenda before Josko Gvardiol came agonisingly close to breaking the deadlock. The defender saw a header saved by Roefs and later struck the post with 16 minutes remaining as City pushed hard for a winner.
Despite the dropped points, Guardiola was pleased with his team's performance. "Really good game, especially the second half," he said. "The first half was really tight, the chances we missed to score a goal in the six-yard box.
"We did everything to win, but in the end we couldn't do it. I'm so proud and delighted with the way we played in this difficult stadium against a difficult opponent."
City had beaten Sunderland 3-0 at the Etihad last month, but this draw extended the Black Cats' unbeaten home league run to 10 games.
Guardiola praised the hosts, adding: "I don't know if teams are able to come here and create what we create. When you are five, six, seven times in the six-yard box, you should score a goal."
Sunderland head coach Regis Le Bris was delighted with another valuable point as his side sat seventh at the halfway stage. "One more good point against one of the best teams in Europe," he said.
"They can score from everywhere, but we defended well and showed bravery with the ball."