United came from behind three times to fight out the extraordinary draw with A-League Men leaders Auckland at Go Media Stadium on Saturday, giving the race for top spot a pulse.
Adelaide fought back from 2-0 then 3-1 down to level the game at 3-3 through two Zach Clough penalties.
Then, Auckland captain Hiroki Sakai thought he'd scored the winner in the 92nd minute, before Bart Vriends bundled home a 98th-minute equaliser.
Adelaide received a penalty - which Clough converted - on the hour mark after a VAR review determined Louis Verstraete caught Ethan Alagich when he tried to challenge for the ball.
"That's very soft," Corica said.
"For me, both penalties are not penalties ... The referee in my opinion, Daniel (Elder), he got both of them wrong."
Adelaide received a second penalty when Tommy Smith legged Stefan Mauk as the midfielder burst through the 18-yard box - with Clough equalising.
"That's a dive," Corica said.
"Of course he is (looking for contact). But that's what the VAR is for. They should know that, and it should have been not given, in my opinion."
Corica pointed to when Auckland last drew with Adelaide, and the Reds were awarded a goal that should have been chalked off.
"The referees the next day said, 'Yeah, you're right. It shouldn't have been a goal.' And I'm sure tomorrow we'll get an apology as well," Corica said.
"But that's not good enough, really, is it?
"When you're talking about top of the table, two big teams trying to win, and not only one decision but two decisions like that go against you.
"It's disappointing."
Auckland (40 points) are eight points clear of second-placed Western United and third-placed Adelaide with eight games to go.
Corica's charges took the lead when Guillermo May cut inside, worked the ball to his left and ripped a wonderful, unstoppable strike past Ethan Cox.
Four minutes later Frances De Vries launched a long throw-in, and with Jay Barnett and Vriends both focused on defending striker Max Mata, May was able to ghost in behind them to bundle home.
Adelaide hit back in the 32nd minute when Archie Goodwin's flick-header from a Clough corner didn't quite cross the line, but Jordan Elsey steamed in at the back post to score.
Auckland extended their lead in the 53rd minute when Logan Rogerson headed home a De Vries corner.
Adelaide struck twice from the penalty spot to set up a show-stopping finish.
In injury time, Cox spilled a close-range effort from Sakai and the Japanese star coolly drilled his second attempt past the goalkeeper.
But Vriends bundled home at the death to snatch a point.
"We'd weathered their storm and we had good control of the game and it was disappointing to concede the fourth late," Adelaide coach Carl Veart said.
"But the response, the boys didn't drop their heads, they pushed and got that equaliser, so very happy in that regard."
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