Christian Eriksen struck after just 11 seconds to give Spurs an early lead at Wembley, before Phil Jones comically hammered the ball into his own net to further cement a dire Red Devils showing.
Pochettino has led Spurs to some big wins in his three-and-a-half year tenure - including a 3-1 victory over European champions Real Madrid in November - but Kane believes last night's win was right up there with the best, according to ESPN.
He said: "I'd say [it's in the] top five performances under the manager. We've had some good performances, especially at home against the big teams, but this one is definitely up there.
"Throughout the game, they never really looked like threatening us. The defence was great -- Jan [Vertonghen] and Davinson [Sanchez] - and the whole team just played well. We had to, because we've got tough games coming up."
The club's Premier League record goalscorer insists they must maintain that level of performance if they are to consolidate a Champions League spot, but added that Man United made it easier for them.
Kane said: "A couple of results went our way this week. We've got to do the same on Sunday. It could have been more. You don't normally get that many opportunities against United. They're normally solid at the back and you have to break them down.
"But obviously getting that goal so quickly opened up the game for us and the only downside was that we didn't score more. Sometimes we say before the game: 'Let's go for this from kick-off today,' and it worked out well.
"From the start, we were winning first and second balls and when we got it down, we kept it. We played some great football, created a lot of chances. It was just a really good game for us and that has to be our focus for the rest of the season - to try to match that."
Spurs travel to Anfield on Sunday in a return to the ground where they were beaten 2-0 last season which prompted Pochettino and captain Hugo Lloris to question whether or not the squad's mentality was strong enough to win the title.
Kane added: "Liverpool are a very strong team especially at home, attacking. They've got some fast players and last year we didn't cope with that very well and we were poor throughout the whole team.
"We can take confidence from today, and this is the performance we need to play against the big teams home and away. We played well against Liverpool at home [in a 4-1 win] and so we have to go there full of confidence."
Spurs added a very fast player to their ranks themselves on deadline day with the capture of Brazilian winger Lucas from PSG, and Kane already believes he will be a great addition to the team.
"Obviously it's a bit tougher for the new lads coming in, but there's no rush," he said. "Hopefully Lucas can come and fit right in and, when he gets an opportunity, take it.
"Playing for a team like PSG, we know what he can do. It's great to have him here and we're looking forward to getting to know him and seeing what he can do in training and games. It's a great addition to the squad."