The Mexican has signed a contract with Valencia until June 2027, with the option of another season if the club qualifies for the Europa League.
Speaking at his presentation, Aguirre explained why he accepted the opportunity at Mestalla.
“You cannot say no to Valencia. They are a historic club in LaLiga and world football, with an incredible fanbase. I have come here as an opponent and it scares you,” he said.
Aguirre also wants home advantage to become a major part of Valencia's recovery.
“I want Mestalla to be an imposing stadium for the opposition, and for the team to return to where it deserves to be.”
The coach was then asked about Gordon, with whom he had a heated but ultimately light-hearted exchange when England defeated Mexico 3-2 in the World Cup last-16.
During the match, Aguirre approached the Barcelona winger and jokingly told him, “F*** you”, a moment that subsequently spread widely on social media.
Gordon later explained that he had not taken the comment as a genuine insult, and Aguirre has now played down the incident himself.
“It was a silly thing, something that came out in the heat of the World Cup,” he said.
“These things happen and I don't give it any more thought.”
Aguirre even suggested he would greet Gordon warmly when the pair meet again.
“There is a very nice photo. I might ask him to sign it for me, actually, for my children. Yes, it's a lovely photo, very lovely. He speaks good Spanish too, the guy.”
The next scheduled meeting between the two comes when Barcelona visit Valencia at the end of January.
For Aguirre, however, the immediate priority is rebuilding Valencia and turning Mestalla back into a difficult venue for visiting teams.