"We met up with him last night at the hotel. He was really rapt, and happy for the whole team."
Boult was also called upon at the death to face two balls from Australian quick bowler Mitchell Starc, when New Zealand were nine wickets down with six runs needed to win.
"We were all pretty nervous at that stage, as was everybody in the crowd. We were nine down with six runs to get."
Boult blocked the first ball he faced then left the next ball to see out the over. Kane Williamson hit a six off the first ball of the following over to claim a famous win for New Zealand.
Mr Boult said he was confident Trent could protect his wicket, and he was actually a handy batsman. "Oh yeah, he can hold the willow."
Although Boult finished with five wickets for 27 runs in his 10 overs - his best ODI bowling record - his father said it was hard to say whether that was his best performance for the Black Caps.
"He's had some really good performances. We were there when he took five wickets for New Zealand in a test match, so it is hard to pick one performance over the other."
Mr Boult said each time his son walked back to his fielding mark during his second spell on Saturday, the crowd would rise and applaud him, which was special to see.
During a press conference after the match, Boult said it was hard to say what was behind his five-wicket haul.
"I'm not too sure to be honest. I have just tried to do what I have been doing over the last five or six months ... pitch the ball up and try and swing it - and I got a bit of luck there with a couple of drag-ons."
Boult's older brother Jono Boult is also a top cricketer and plays for Northern Districts.
Boult spent his early years in Rotorua, before his family moved to Whakatane when he was 5 or 6 and then Tauranga. The family are still based in Tauranga.