The Blues goalkeeper stubbornly refused to leave the Wembley pitch in the final minute of extra time before City triumphed in a penalty shoot-out.
Manager Maurizio Sarri was attempting to bring on number two goalkeeper Willy Caballero, but cancelled the substitution when Arrizabalaga sensationally flouted the order.
And City skipper Kompany joked that he would have liked the option to resist being brought off during his career.
"Of course I've never seen it,” he told Sky Sports. “I wish I could do it every now and then when I don't want to get subbed off.”
Argentine Caballero, who was the hero when City beat Liverpool to life the Cup in 2016, had been Sarri’s choice to face penalties after the game finished goalless, but in unprecedented scenes found himself returning to the bench moments after stripping off ready to come on.
"I know how good Willy is on penalties,” said Kompany. “When we won this competition against Liverpool he was tremendous, he won the penalties for us and it would be another mind game to be played.
"It didn't happen and the confidence was there to score the penalties."
Former Chelsea skipper John Terry, who lifted the Cup under Jose Mourinho in 2005, said he would be surprised if there were not consequences for Arrizabalaga after publically disrespecting his manager’s wishes.
"It will be interesting to see if Kepa plays the next game,” said Terry. “If I was in the dressing room I would expect the manager to come in and deal with it straight away.”
The stand-off represented a bizarre development in the increasingly uncertain saga of Sarri’s tenure at Chelsea.
Some reports had suggested that the Italian would be sacked if the Blues lost Sunday’s showpiece.
The road doesn't get any easier as Sarri and Chelsea face Tottenham midweek.