Early goals from Izale McLeod and Gabor Gyepes had put Pompey 2-0 up but Adam Webster's own-goal and Darren Potter's 72nd-minute equaliser stretched the Dons' unbeaten run to six games.
"We said at the start of the week we would have taken seven points," said Appleton, whose side beat Scunthorpe and Yeovil in their last two matches.
"We had two very good victories and we've come here and had a right go at them first half. We ran out of steam a little bit towards the end but I thought we thoroughly deserved a point, if not probably three points.
"We played some really good stuff, we did have a game plan that worked really well for half an hour."