The visitors rarely threatened during a drab Premier League affair at the Stadium of Light, with Gylfi Sigurdsson registering Swansea's only shot on target with a tame second-half strike.
Swansea had Angel Rangel sent off for a second bookable offence in the 81st minute, before Sunderland substitute Steven Fletcher almost snatched the three points when he headed wide of the left-hand post.
But Monk, who saw a player dismissed for the second time in as many Premier League matches, insisted that - under the circumstances - the draw was a good result.
"It was definitely a good point the way the game panned out and going down to 10 men," he is quoted as saying by BBC Sport. "We showed character in adversity and I thought the boys defended admirably and we deserved a point.
"They had a couple of headers and when we were down to 10 men threw a lot forward but apart from that we limited them to hardly anything.
"We weren't as fluid as we have been but there will be games like that and then you have to do the basics right."
Swansea, who have taken 10 points from their opening six matches, host Newcastle United in the Premier League next Saturday.
