Kane scored the second goal in Spurs' 2-0 win over Watford at Wembley in front of England boss Gareth Southgate to help boost Tottenham's chances of securing a top-four finish.
Neville explained: "When Jose Mourinho's time is finished at Manchester United, whether that is one year, two years, I hope it's three years, I hope he wins multiple Premier League titles because I think he's a fantastic manager".
"Of course the most important thing for us is to win the three points because it puts us in a very important position in the table".
Spurs nearly had a third in the 68th minute when Belgium defender Jan Vertonghen met a Trippier free-kick but his header came back off the post, while Kane had an effort ruled offside and substitute Moussa Sissoko fired over from close range.
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"Three games ahead, I think we are in a good situation".
It was far from a vintage performance from Pochettino's side, though, and they were reliant on Lloris to pull off a number of saves to keep his side in the lead.
Spurs: Lloris, Trippier, Vertoghen, Sanchez, Son (Sissoko, 74), Kane, Dier, Dembele (Wanyama, 62), Alli (Lamela, 81) Eriksen, Davies. Watford were free to play, no pressure, they are safe, for us it is a massive pressure to take three points.
He then produced a disappointing performance in the FA Cup semi-final against Manchester United, leading to an official FA Twitter account mocking him with a video that suggested Kane had been in Chris Smalling's "pocket" for the entire game.
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But the forward, who now has 27 league goals and 38 for the season, can cope with criticism as he tries to catch Liverpool's Mo Salah (31) for the Golden Boot as Premier League top scorer.
"I feel good", he said.
"I would have liked to play better over the last few games but the whole team would have liked to do that", Kane said.
Pochettino guided Spurs to a third place finish in 2015-16, before going one better to finish as runners-up behind Chelsea last season.
The Sky Sports pundit remarked during the programme: "Pep Guardiola, the way I should judge him, should he win the league?"
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