It was tempting to say that Ralph Hasenhüttl now knows the scale of the challenge that faces him at Southampton but the truth is the new manager was already painfully aware. Relegation-threatened clubs are queasily placed for good reason. They call for fresh direction in the middle of a season because they are desperate.

There were familiar flaws for Hasenhüttl to digest from his seat in the Wembley stands, having been confirmed as Mark Hughes’s successor in the morning – namely, defensive looseness that added up to the softest of concessions and, at the other end, a lack of discernible goal threat until Tottenham were 3-0 up and the game was over.

Time, of course, is short for Hasenhüttl. His first match comes at Cardiff on Saturday and the club will pray for a new-manager bounce. His presence did not inspire one here, although Southampton – under the caretaker charge of Kelvin Davis – did enjoy a decent final half-hour, when Hugo Lloris was forced into a succession of saves. To repeat: the game was over by then.

Mauricio Pochettino described Lloris as the man of the match, which was strange, but it was a strange kind of occasion, played out in front of only 33,012 – comfortably Spurs’ lowest attendance for a Premier League game at Wembley. Their regular followers are sick of playing here.

Tottenham were able to bounce back from their 4-2 defeat at Arsenal on Sunday, with Harry Kane putting them in charge with his 13th goal of the club season and Lucas Moura and the excellent Son Heung-min giving the scoreline its gloss.

Davis could be proud of how his players kept going, with Lloris making his saves and the substitute, Mohamed Elyounoussi, heading against the crossbar in stoppage-time before another replacement, Charlie Austin, ran through to score. But no team can defend this generously and expect to emerge unscathed.

“I think it’s a mindset,” Davis said. “I don’t know whether it’s confidence. If you look at the goals we conceded, they’re ultimately easy to stop. It’s something the new manager will be looking to address as quickly as he can.”

Spurs switched off at 3-0 but the biggest blot on their evening was the groin injury that forced off Kieran Trippier. He was replaced by the 18-year-old Oliver Skipp, for whom it was a Premier League debut.

Pochettino said that Trippier’s problem was a legacy of the one he suffered for England in the World Cup semi-final against Croatia. He felt the suspect Wembley surface had done the full-back no favours.

Hasenhüttl had flown into London and he addressed the club’s staff at the team hotel but he kept his distance from the players, paying Davis the respect of not interfering with his preparations. Davis has been named as his assistant coach.

“He was very concise with his information and he explained how he wants to work,” Davis said. “There was a good feel to him. It was quite simple – how he likes to play the game, how he likes his sessions to be planned, how he watches opposition, what he expects in terms of standards.”

Southampton made a false start. After Son had stuck the post with a volley, the visitors’ defence switched off on a Spurs corner. Trippier played it short to Christian Eriksen, he crossed and nobody tracked the run of Kane.

Southampton stabilised and they would have been level midway through the first half but Pierre-Emile Højbjerg’s fizzing drive from 25 yards hit the inside of the post and Stuart Armstrong was offside on the rebound. It looked as though Lloris had got his fingertips to the shot. Southampton had some good spells of possession but cutting edge is what they wanted.

Spurs looked as though they would score more before half-time, with Alex McCarthy making one particularly smart save to deny Son, and they did score more after the interval. Steven Davis failed to clear Trippier’s corner and Lucas lashed home at the second attempt. The third came when Trippier won the ball from Matt Targett; Kane crossed and Son tapped home.

Cue the Southampton flurry. Maya Yoshida somehow failed to touch home James Ward-Prowse’s free-kick, Lloris made a double save to deny Højbjerg and Ward-Prowse while he also thwarted Austin. The striker would find a way through with virtually the last kick but, by then, Southampton’s thoughts were turning to Cardiff.