Beattie's side reacted angrily following Padovani's fierce challenge in the centre circle after 30 minutes.
Referee Chris Sarginson booked the Pompey player, but former Southampton striker Beattie checked a video replay of the incident and felt the Frenchman should have been dismissed.
Jake Jervis sealed victory for Pompey with the only goal after 48 minutes when he cut inside from the left and lashed a low drive into the bottom corner of the net.
But Beattie was dejected to see Accrington leave the south coast empty-handed and insisted they should have been facing 10 men for the last hour of the match.
"The lads are not happy with the referee's decision not to send Padovani off. I've looked at the video and it's a joke of a decision," said Beattie.
"I'm lucky not to be going to see Peter Murphy in A&E at the moment with a broken leg.
"The ref took too long to make the decision and he was thinking 'I don't want to be battered by 13,000 fans for the rest of the game.' So he gave him a booking.
"The players are unhappy about the nature of the tackle. Padovani made absolutely no attempt to play the ball and his knee was turned to his side so he could show the bottom of his foot to Peter's leg. The lads are incensed to be quite honest and I think they've got every right to be."
However, Beattie took some solace from Stanley's efforts in the match.
He added: "We were unlucky not to get something out of the game. The lads got punished for one of the few mistakes they made, and punished in the most severe way. I just can't fault their effort, they played well and the best side lost."