The Hoops looked destined for defeat until Richard Dunne put through his own goal in the final seconds - Stephen Warnock's clearance catching him unawares and flying in.
There had been controversy before that, though, with Villa taking the lead through Barry Bannan from the spot after Armand Traore was adjudged to have pulled Gabriel Agbonlahor's shirt.
Traore was booked - something Warnock disagreed with - and was then sent off for a second incident - his manager agreeing on this occasion.
But the coach was angry at Oliver's decision to award the initial penalty and his failure to award two spot-kicks to his side for what he believed to be handballs by Alan Hutton.
Speaking to Sky Sports 1, Warnock said: "That's the character and spirit that got us promoted. We're in the top league, and are never say beaten (sic).
"We're all disappointed at the decisions obviously, but I think we responded in the right way. I think there could have been a couple of Villa players sent off for offences, two bookings.
"I think Traore was a little bit thick and naive, but we don't make a meal of it, we don't try and con the referee or anything.
"They've (Villa players) stayed on the pitch, (James) Collins and the number 10 whoever he was (Charles N'Zogbia), should have been booked twice.
"It's disappointing to be talking about referees...there's nothing to referee in that game. Not one Aston Villa supporter appeals for a penalty. I bet there are 25,000 more tugs on that pitch.
"Referees should be seen and not heard but it takes away from our performance - I thought we were superb."
Warnock went on to suggest he felt Hutton would have been penalised were he playing at other grounds.
He added: "I don't think it would have been a penalty at a lot of grounds and I think we would have got a penalty on certain days. They thought they'd won it and we kept going."
Warnock was speaking straight after the final whistle and, in an unusual move, returned to face the cameras for a second time having reviewed the incidents on tape.
He remained angry Hutton was not penalised for his 'block' of a Tommy Smith cross, adding: "How has the linesman not seen that? He deliberately handballs it.
"And the second one, we're told that if you raise your hands it's a handball. He's raised his hands against Tommy Smith.
"But the first one is embarrassing. How that cannot be given a penalty...he can't even say he's in a bad position.
"My boys deserve better than that. Traore's penalty, come on, I've never seen anything like that. He blows on him. He wants to give the penalty and it's wrong."
Villa manager Alex McLeish had less to say than his opposite number, but felt Oliver had got the Agbonlahor call right.
"I was surprised nobody complained," he said.
"Not a lot of Villa hands went up. I thought Gabby was impeded, but I'd have to see it again."
On his side's performance, the Scot added: "I told them a few home truths at half-time as it was very poor in the first half.
"We were chasing shadows, insipid and it was not a Villa performance. I let them know and sure enough, we got a lot better performance."
Source: Team Talk
Source: Team Talk