Iain Hume's 11th-minute strike and a bizarre own goal from Jay McEveley three minutes after the break saw North End make it nine league games unbeaten with their fifth win in a row.
Dany N'Guessan's curling effort from the edge of the area, with four minutes remaining, gave Swindon hope of a comeback but Preston hung on.
"Naturally, I'm really frustrated," Cooper said. "We looked very lethargic for large parts of the game, and I think the efforts of the other night (Tuesday's 2-0 Capital One Cup defeat to Chelsea) took it out of us.
"Preston were in our faces and very physical and we didn't deal with it particularly well. If we'd started the game as well as we finished it then it may have been a different story, but that's not good enough.
"We didn't pass the ball properly and we didn't match Preston, and we conceded another two sloppy goals which is what it's all about at the end of the day. You can't concede goals like that and expect to win football matches.
"The second was a real comedy goal, and between them they've got to sort it out. They have to deal with the situation better than that because Preston have scored a goal there without even trying."