Pompey went close to scoring when a superb long-range effort from Akos Buzsaky struck the woodwork and Scott Allan also had a shot blocked. But Nick Blackman struck the winner from the penalty spot in the 66th minute after Lubomir Michalik's reckless sliding tackle felled Chris Porter inside the area.
"I thought we were very, very good for large periods of the game," Appleton said.
"I thought there were some really good performances and we had them on the back foot. We caused them a lot of problems and it was harsh to lose the game.
"A crazy little bit of defending from Lubo cost us at least a point. Even if he doesn't touch him, he was daft enough to go to ground when he didn't need to. He (Porter) was going away from the goal and it was just a rush of blood to the head."
Appleton was pleased with Allan, who also had a spell at Pompey last season, after the player only arrived on loan from West Brom earlier in the day.
"I thought he was outstanding in the first-half," Appleton added.
"He was almost unplayable at times. He tired a little towards the end because he's not had much football. He's going to be a big, big plus for us over the coming month."