"Look, we're a bunch of Kiwis. There's only five million of us, so we're obviously very proud to be representing our country," said man of the match Mitchell.
"We've had some success in the last few years. We're going to enjoy the win tonight but then we move on pretty quickly.”
"We know that we have a final on Sunday, and whoever we're taking on should be good fun."
New Zealand will take on Australia or Pakistan in the title clash on 14 November in Dubai.
Mitchell, who smashed four fours and four sixes in his 47-ball blitz, is playing in his first T20I World Cup after his international debut in 2019.
After Neesham's wicket, Mitchell smashed Chris Woakes for two sixes and one four to trigger celebrations in the dugout.
"It's obviously a great honour to represent my country at a World Cup," said Mitchell. "If you said this five, six years ago I would have laughed at you, so to be here sitting right now is awesome."
New Zealand were in early trouble at 13-2 with Martin Guptill and skipper Kane Williamson back in the pavilion.
Mitchell and Devon Conway, who made 46, then put on 82 runs for the third wicket but runs were still hard to come as England rotated their bowling options.
Glenn Phillips was out and New Zealand slipped to 107-4 when Neesham walked in and changed the course of the match alongside Mitchell as the pair put on 40 off 17 balls.
Mitchell said at no point did he believe the target was out of reach.
"No, it probably sounds weird, but it never felt like it was out of our grasp," said Mitchell.
"I think especially with that smaller side boundary on one side, we knew that there were going to be matchups there that might suit us towards the end.”
"I thought the way that 'Neesh' came out and really dominated that one over really set the momentum heading into those last few, so yeah, take my cap off to him. He played a hell of a knock."