Argyle, promoted back to Sky Bet League One last season, reached the fourth round for the first time since 2008.
"It's massive for me," said Lowe. "It's the best competition in the world that we, or I as a manager, will ever enter.
"I respect it massively. I'll watch the highlights on TV tonight with my lad."
Skipper Joe Edwards struck Plymouth's 70th-minute winner after they had twice been forced to come from behind against a second-string Huddersfield side.
Romoney Crichlow and Aaron Rowe both scored their first senior goals for Huddersfield to twice give the West Yorkshire club the lead in the first period.
But Plymouth responded each time through Ryan Hardie and Panutche Camara before Edwards struck their winner.
Lowe added: "It was a great performance by our lads – I thought they were brilliant in everything they did.
"We counter-attacked very well and scored three fantastic goals. When you're beating a Championship side, it's pleasing.
"When the opposition make as many changes as Huddersfield did, it's never easy."
Lowe, born in Liverpool, refused to say who he wanted to play in the next round.
"I'm not telling you, because every time I say someone I never get them," he added. "I'm going to sit back and enjoy it – and whoever we get, we get."
Huddersfield made clear where their priorities lie this season as boss Carlos Corberan made 11 changes to the side which started last week's home defeat to Reading.
Centre-half Mustapha Olagunju, 19, and 17-year-old winger Pat Jones made their first-team debuts, while Spanish midfielder Alex Vallejo, Josh Austerfield and striker Kieran Phillips all made their first starts.
Corberan said: "I think there is a little bit of everything. First of all we didn't get the result, we wanted to win because it was important for us to continue in this competition.
"Even if we used the competition to continue, for more of these experiences to grow our squad, it was important we continued."
Corberan, who worked as Leeds boss Marcelo Bielsa's assistant before taking on his first manager's job last July, also handed debuts to substitutes Myles Bright and Etienne Camara.
"It was a big positive for some of these players that they were playing today," Corberan added. "There were positives and things we need to improve on.
"Our ambition for the rest of the season is to be a more competitive team than we have been in the Championship."