Mr Joyce was giving a speech in Perth on Tuesday when the man walked on stage and shoved the pie in his face.
A man identified by local media as the attacker later criticised the airline chief's support for same-sex marriage, which is not legal in Australia.
"I will have every intention of pressing charges," Mr Joyce said.
Police charged the 67-year-old man with giving false details after the incident, which happened in front of 500 people. He may yet face an assault charge, police told the BBC.
"On the west coast, there is very limited opportunity to have connection with national figures," the pie-wielder, identified as Tony Overheu, told the Australian Broadcasting Corp.
"From my reading, it would appear that Alan Joyce is very much part of a network trying to subvert the federal parliamentary process around the issue of marriage equality."
Mr Joyce was one of 20 company chief executives who signed a petition in March calling on Prime Minister Malcolm Turnbull to legalise same-sex marriage.
Immigration Minister Peter Dutton, the government's most prominent conservative, described the attack as "a disgrace".
"The person should be ashamed. The threats any of us receive is unacceptable," Mr Dutton tweeted.
Mr Joyce had been discussing the airline's recent decision to operate non-stop flights from London to Perth when the incident happened.
"I don't know what that was about," he said, before continuing his speech.

Footage from the area shows a huge column of lava and ash being sent several kilometres into the air.
The authorities have declared a red alert and evacuated more than 4,000 people within a 20km (12 mile) radius.
The Calbuco volcano is one of the most active in Chile, but its eruption took officials in the area by surprise.
Alejandro Verges, an emergency director for the region, said Calbuco had not been under any special form of observation.
Calbuco eruption: your pictures
The inhabitants of the nearby town of Ensenada - along with residents from two other smaller communities - have been ordered to evacuate their homes.
Schools in the area have been shut and some flights cancelled.
The nearby city of Puerto Montt - a gateway to the popular Patagonia region - has already been blanketed in a cloud of ash.
TV footage showed traffic jams in the city and long queues at petrol stations. The nearby town of Puerto Varas was also under a state of alert.
Mayor Gervoy Paredes said residents were "very, very frightened".
"I had never seen this before. It scares you in the beginning. You start to wonder what is going to happen to you," said one unnamed woman.
"Everyone starts to think about gathering water and I don't know what. We got together with the neighbours to see what we would do and wait for news over the radio because we knew that they were evacuating Ensenada and other places near the volcano."
Interior Minister Rodrigo Penailillo called on people affected to "remain calm and stay informed".
Neighbouring Argentina has also put emergency measures in place for the city of Bariloche - about 100km from Calbuco - where ash clouds are expected.
Residents there have been warned to stay indoors.
Chile has the second largest chain of volcanoes in the world after Indonesia, with about 500 that are potentially active.
It is southern Chile's second volcanic eruption in as many months.
In March, the Villarrica volcano erupted in the early hours of the morning, spewing ash and lava. The authorities say this latest eruption is more serious.
Qantas chief executive Alan Joyce has said he intends to press charges against a man who hit him in the face with a pie.
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The Calbuco volcano in southern Chile has erupted twice in the space of a few hours - having lain dormant for decades.