Mauricio Pochettino's men looked to have turned a corner at their new base after Wednesday's pulsating win over Borussia Dortmund but this result means they are still winless here in the league this season.
Of all teams who Spurs have faced 10+ times in the Premier League, they have their highest win rate (83.3%) and goals-per-match average (2.33) v Swansea.
Mauricio Pochettino has long since exhausted of questions about Spurs' domestic setup but had to go through it all again and could not dispel the suspicion that all the talk risks becoming self-fulfilling.
Spurs registered eight shots on target to Swansea's zero.
"The reality is that we dropped a lot of points after three games but I am not anxious", he said. "We still need to improve a lot, but we are in a great way and the last two victories will help us". He had freshened up his starting lineup with Kieran Trippier, Moussa Sissoko and Dele Alli, moving Son Heung-min to left wing-back for the first half, but the effect had that wearyingly disjointed post-Champions League feel.
The Spurs full-back has had a brilliant start to the season, scoring once, setting up two goals and keeping two clean sheets.
'At the very last minute Pochettino called me and convinced me [to join Tottenham].
"I am trying to focus on the pitch, trying to help the team, give my quality on the field - that's important and the rest will come", Alderweireld said in an interview with talkSPORT. We didn't create any real chances, but we have to think that's a good point.
Tottenham should have been awarded a penalty in the dying stages when Serge Aurier was brought down inside the area by Jordan Ayew, but Mike Dean instead bizarrely booked the full-back for handball.
"In contrast, Swansea really struggled against Newcastle".
"It is true after the draw to say well done to Swansea and congratulate them for taking a draw", he added.
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.