Allardyce said: "While you never want to see anybody sent off, the inconsistency in that department has played a part tonight.
"There have been much lesser opportunities than that where people have had the chance to score a goal and been felled and a red card has been shown, but this time Stelios has gone round with only about six yards in front of him and an open goal and the keeper has stayed on the pitch.
"I am disappointed. We've missed a few chances and the penalty was the big one, especially as it came from the player who showed so much accuracy in scoring our goal direct from a free-kick.
"This is possibly the weakest team I've put out this season, what with so many away at the African Nations Cup.
"We could get a couple back later this week but Fadiga might have been out there as well but for the injuries he's had with his knees.
"Once we got our noses in front we should have done better to see off a late rally but then Pompey put on the big lad [Azar Karadas] and threw everything in our box and in the end it has cost us two points.
"I can't complain about the performance of the 11 lads on the pitch overall but we've missed top players even though we haven't been beaten since before the third-round FA Cup tie at Watford."
Allardyce also paid special tribute to Matt Jansen, who was given his full debut and not only impressed with his performance but with his staying power.
"I thought he was going to pinch the headlines," Allardyce said.
"That would have been great for us but even more important for him.
"He had a very good game but, unfortunately, wasn't able to pop up with that goal which would have made it a brilliant win for us and a brilliant start for him.
"We didn't expect him to quite do the full 90 minutes but he battled his way through."