White came on for the final 14 minutes of Scotland’s first-Test defeat by the Pumas in Jujuy on Saturday, just before Emiliano Boffelli’s penalty sealed a 26-18 victory.
The scrum-half is on his first Scotland tour and is looking to provide the same type of impact as his international debut, when he claimed a try during a brief first-half appearance in the 20-17 win over England in February.
White was on the field for 12 first-half minutes while Ali Price was assessed for a head knock, before coming back on later in the game at BT Murrayfield.
And the memory of the reaction to his try and the victory is still spurring him on during his first Scotland tour.
“It was a moment that I will never forget,” the London Irish player said in a video interview on the Scottish Rugby Union’s Twitter account.
“Genuinely, I can just close my eyes now and picture the whole place erupting. It was special, it meant a lot to me and my family.
“It was amazing and the messages I got after from Scottish people and fans, just how happy they were, it was amazing.
“The main thing for me is that every time now that I pull on the shirt, I want to do everything I can to make sure that I give those people who want us to do so well the same. I want to make sure I do everything I can to give the nation that joy that they had that day.
“I know how much it means to people and how much it means to me.
“Every time is a complete honour and something I will never take for granted. I will love every minute and just want to do well every minute and I will give my all.
“It was an incredible moment and it has just made me want more and want to do better and make sure we get more results like that in the future.”
Scotland will have to improve on their first-half display when they take on Argentina in the second game of a three-match series on Saturday.
Blair Kinghorn hit two penalties but Scotland struggled to make inroads with ball in hand and conceded two tries late in the half to leave them facing an uphill struggle after the break.
White said: “It’s a bit frustrating in terms of the fact that we probably didn’t get across what we wanted to do or how we trained.
“So in that respect it was a bit frustrating not to show the way we wanted to play and the tempo that we wanted to play at.
“Credit to Argentina, they were good in areas and they came alive with counter-attack ball that we gave them.
“So we know what they are going to bring but we need to outwork them, both physically and, also, when we have the ball, play at a higher tempo than them.
“I think that’s the main thing going into the weekend, to play at a higher tempo and to run them about.
“As a squad, we have some brilliant players here and a real close connection, so as a group we are more than capable enough to go and beat them at the weekend.
“We just need to make sure we are constantly on it and focused for 80 minutes and put together a performance we can all be proud of.
“We have reviewed ourselves pretty harshly and we want to correct the wrongs that we did at the weekend and make sure that, this weekend, we take it to 1-1.”