Romero stopped two spot kicks as Argentina beat Van Gaal's team 4-2 in a penalty shootout in the World Cup semifinals, advancing to the final against Germany.
''I taught Romero to stop penalties, so that hurts,'' said Van Gaal, who worked with Romero at Dutch club Alkmaar in 2007-2009.
Romero praised his former coach for helping him adapt when he arrived in the Netherlands as a 20-year-old, though he said winning the shootout came down to chance.
''It's luck, that's the truth. You can dive (the right way) and not make it, like happened to their goalkeeper,'' Romero said. ''I had confidence, thank God things turned out.''
Romero, who isn't even a starter in his current club team Monaco, now has three straight clean sheets in the World Cup, and has only conceded three goals in the tournament.
The 27-year-old goalkeeper said a lot of thoughts were running through his mind before the shootout.
''I had my colleagues from the bench helping me where each player could shoot,'' Romero said.
He stopped Ron Vlaar's penalty kick by diving right and Wesley Sneijder's by diving to the left.
''I was thinking Sneijder was going to shoot there,'' Romero said. ''I was also thinking that (Arjen) Robben was going to shoot to my left and then he ended up shooting to the other side and that's why I was so mad.''
Argentina coach Alejandro Sabella said Romero keeps a folder of information on other teams and their players and where they normally aim their penalties.
Before the World Cup, Sabella insisted he still considered Romero as his top choice despite his lack of playing time in the French league.
Romero said he had learned a lot both from Sabella and Van Gaal, and that he went to greet the Netherlands coach in the dressing room after the game.
''He is someone that helped me a lot when I arrived in Holland, in a completely different country with different customs,'' Romero said. ''I will be forever grateful to the coach for helping me out in a country that is so different from ours.''