Spurs were left frustrated as Harry Kane hit the bar and Swansea keeper Lukas Fabianski made a string of good saves to leave the hosts still winless at Wembley in the Premier League.
Swansea have never beaten Tottenham in the Premier League. Needless to say, the Jack Army know how much of a loss Gylfi Sigurdsson and Fernando Llorente could be.
A dogged Swansea were worthy of their point despite failing, for the third time this season, to have a shot on target.
"At the very last minute, Pochettino called me and convinced me [to join Spurs]", the former Spanish worldwide told Daily Mail.
Now whilst talking about Kane, Neville echoed this sentiment by telling BBC Radio Five Live as reported by The Metro, "He could have to leave Spurs to become that real top, top, world class [Robert] Lewandowski type player, he could".
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Tottenham have already dropped seven points from three games in front of their own fans this season - more than they did in the entire 2016-17 campaign at White Hart Lane - but Pochettino played down the significance of their dip in home form. I think he is doing fantastic, Harry Kane. "I really want to contribute and I hope that I can score a lot of goals to help the club and meet our objectives".
Serge Aurier could have earned a late penalty when he went down under the slightest of clips from Jordan Ayew, while Martin Olsson was twice fortunate not to concede a spot-kick, once after blocking Toby Alderweireld and then for touching a loose ball with his hand.
Swansea's point pleased Paul Clement, who had been concerned by what he called a "complacent" performance in last Sunday's defeat by Newcastle.
But it was Swansea who threatened to get it. Swansea had barely got out their half but they served up a reminder that they posed a threat on the counter-attack during a rare foray forward in the 25th minute. They offered next to nothing going forwards bar a first-half glimmer when Tammy Abraham, leading the line with maturity, created an opening for Tom Carroll that Sissoko quickly snuffed out.
This was Tottenham's first clean sheet in a game at Wembley since the 2009 League Cup final against Manchester United, having conceded in their previous 11.