Hasenhuettl, who will take over from interim Kelvin Davis, who becomes the new manager's No. 2, will have been encouraged by the final 30 minutes as Southampton were the better side and grabbed a late consolation through Charlie Austin.
51-year-old signed with the saints a three-year agreement.
The Saints hit the frame of Hugo Lloris's goal on three separate occasions but gave the hosts a helping hand with Harry Kane, Lucas Moura and Son Hueng-min goals.
'I can guarantee you that when you see us playing in the summer it will be different than when you see the team now, ' he said.
"We had a few chances but in this best period we almost made an own goal".
MORE SOUTHAMPTON STORIESMARCHING ON When is Tottenham vs Southampton and can I watch it on TV?
"In the same way I try to understand, it was a tough evening, hard to play the three emotional games we played last week, you play, it is not easy to feel fresh in your legs or your mind".
Spurs goalkeeper Loris somehow got his fingertips to a swerving effort from Pierre Hojbjerg and tipped it on to the post.
Skoda Scala revealed as VW Golf and Ford Focus rival
Five- and six-speed manuals and a seven-speed dual-clutch automatic transmission will be offered, depending on the powerplant. On the outside, the new hatchback borrows many of its features from the Vision RS Concept that debuted in Paris this fall.
The Premier League match between Cardiff and Southampton will be broadcast online.
The new Southampton boss makes his Premier League bow in Cardiff against Warnock, a man who has overseen more than 1500 games on these shores.
"At first I think the squad is very big so we have a lot of positions where we have too many players and maybe one or the other is leaving us and we bring something new".
"We know each other and we were sat our Federation Internationale de Football Association pro-licence tests together".
Southampton (P13, W0, D7, L6) are now on their longest winless run in all competitions since October 1998 (also 13 matches).
The England striker scored a hat-trick in this fixture last season and has now scored seven times in his last six league games against Saints.
Southampton have won just nine points from their opening 15 games this season.
Tottenham's Oliver Skipp (18 years and 79 days) is the youngest player to debut for the club since Gareth Bale against Manchester United in August 2007 (18 years and 40 days).