Both managers thought neither of the two penalties converted by City's Steve Davies and Thomas Ince for the Seasiders should have been awarded in the final 10 minutes.
Appleton felt robbed by Ward's decision to penalise Blackpool goalkeeper Matt Gilks for bringing down Albert Adomah, who looked to have overrun the ball out of play after 81 minutes at Ashton Gate.
He said: "To say it was soft is being kind. The ref took four or five seconds to make up his mind and seemed set to award a goal-kick before the home fans reacted.
"It was frustrating to fall behind because we had squandered several great opportunities to score. But the spirit the lads showed to fight back was great.
"I'm just grateful a linesman was on the ball for our penalty. It looked a clear handball to me, but I'm not sure the ref would have given it if he hadn't seen the flag.
"We need to be more clinical in our finishing, but I am happy with the way the players are responding to what I want them to do."