Spurs went into the match having seemingly banished their Wembley woes with victory over Borussia Dortmund in the Champions League on Wednesday, but they failed to find a way through Swansea's resolute rearguard action.
Paul Clement's side bounced back from defeat to Newcastle United last weekend to hold on for the point, and Abraham is delighted with how the visitors performed.
"It's a fantastic result. We knew what we were coming into and that there'd be limited chances. We stuck together and fought until the end," he told BT Sport.
"We came in at half time saying we had to stay in the game and that's what we did. It was scary watching it from the sides at the end but I trusted the boys."
The draw leaves Swansea 14th in the Premier League table with five points from as many games this season.