Abraham - on loan from Chelsea - struck what proved to be the winner in the eighth minute with a superb header from Ahmed Elomohamady’s cross.
Norwegian keeper Nyland, who has struggled to make an impact since his £3m arrival, also emerged with credit after making a number of top-quality saves.
“Tammy is a handful and he knows better than me that he should have been walking away with the match ball," Smith said.
"Tammy put in a hell of shift up front on his own and proved that he is a fine player.
"In the second half I thought our energy levels dropped and allowed Swansea to get onto the ball in little pockets.
“My goalkeeper made some very good saves. The clean sheet is a big thing for us having conceded a lot of goals this season. Nyland can take a lot from this game.
“It’s a tough league but a tight league. The win gives us an opportunity to move forward. We now have two away games but the players know what I expect.
“It is always a good start when you get three points. I thought we were very good in the first half, certainly the first 30 minutes we stuck to the game plan.
"We won the ball back in key areas but didn’t convert the opportunities created.
“It was great to give the fans the win. It was one of the biggest crowds of the day including the Premier League. It just shows what can happen at this club if we have a plan to move forward.”