The Pole made good saves to deny Adam Johnson and Santiago Vergini at the Stadium of Light, while his side's backline were forced into a rearguard action when Angel Rangel was sent off with nine minutes to play.
"We were in a difficult situation near the end with the red card, but managed to get something from the game," Fabianski told the club's official website. "There were a lot of set pieces and balls into the box. but I thought we dealt with that threat very well.
"Federico is a new player in English football and he had a different game to face today, with plenty of crosses and physical play. But he and Ash did really well and it was a good point for us in the end."
Swansea are fifth in the Premier League with 10 points from their six matches this season.