Martinez labelled the match official "useless" after Argentina's dramatic penalty shootout victory over the Netherlands.
The goalkeeper was the hero, saving from Virgil van Dijk and Steven Berghuis as La Albiceleste prevailed 4-3 on spot kicks after a 2-2 draw, in which they surrendered a 2-0 lead.
The performance of referee Antonio Mateu Lahoz was a huge talking point at Lusail Stadium; the Spanish official issuing 16 yellow cards during the ill-tempered affair – the most cautions in a World Cup match – and one red.
He also added 10 minutes at the end of regulation time, in which the Netherlands scored a dramatic last-gasp equaliser through Wout Weghorst to force an additional 30 minutes.
🇳🇱 v 🇦🇷 ⚽️ 90+11' Incredible. @OnsOranje has equalised in stunning fashion with super-sub Wout Weghorst slotting home after an audacious free-kick caught @Argentina by surprise. #NED 2-2 #ARG | Follow it LIVE HERE 👉 https://t.co/GsfF6noOyX#FIFAWorldCup #NEDARG #Qatar2022 pic.twitter.com/v83DvvYGlI— beIN SPORTS (@beINSPORTS_AUS) December 9, 2022
"The referee is useless. Hopefully, we don't have that referee anymore," Martinez said, before dedicating the victory to his compatriots.
"The first thing that comes to mind is emotion.
"I do this for 45 million people. To give people such joy is the biggest thing right now. We are in the semi-final because we have passion and heart. We are excited, as are the people."
Namesake Lautaro Martinez, who netted the decisive spot kick, said: "On that walk to the point of the penalty, I was very calm because I trust my work. When I caught the ball, I thought about my daughter. She changed my life."
🇦🇷❤️ Another game closer...— FIFA World Cup (@FIFAWorldCup) December 9, 2022
Alexis Mac Allister is expecting a "very tough" semi-final clash with Croatia, which stunned Brazil on penalties in the opening quarter-final, while Rodrigo de Paul is embracing the moment.
"I'm excited because I work hard to make these things happen," the midfielder said.
"Playing a World Cup semi-final is not an everyday occurrence.
"The idea was to come the first day and leave on the last day. We rose from a defeat at the beginning.
"Hopefully, these moments that are incredible keep coming. I tell people to enjoy it because this belongs to everyone."