I have seen some good things from my team but we made too many mistakes.
Lax defending from Southampton allowed Spurs to take a ninth-minute lead.
"We started the second half really well", said the Argentine.
"Lloris was man of the match and that's something I'm disappointed about".
He added: "What we have to do is try and work out a formula where we take our chances away from home and try and defend better. However, I feel it was job done and I'm happy with the three points".
However, a busy period of fixtures, starting with Saturday's trip to fellow strugglers Cardiff City, means Hasenhuttl will get little time to work with his players on the training field in the coming weeks.
Spurs goalkeeper Loris somehow got his fingertips to a swerving effort from Pierre Hojbjerg and tipped it on to the post.
"We've improved almost weekly".
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"While we're here the fans have been fantastic".
Hasenhuttl has now officially taken charge following the 3-1 defeat against Tottenham at Wembley on Wednesday night.
Southampton, who are 18th, are now winless in 13 matches in all competitions, their longest such run since hitting the same number between May and October 1998.
- Southampton have earned just nine points from their opening 15 games this season; just three of the previous 18 teams to have nine points or fewer from their first 15 games of a Premier League season have avoided relegation. Both teams enter the weekend in the middle of a relegation battle.
Tottenham playmaker Christian Eriksen has provided at least one assist in each of his last three Premier League games (four total), the first time he has done so within a single campaign since April 2016.
"We have been aware of Ralph since his days at FC Ingolstadt, where he showed the qualities that we believe we need at the club", said Krueger.
Warnock was delighted with Paterson's contribution, but also credited referee Moss who waved play on after Oriol Romeu clattered into Victor Camarasa just seconds before the goal.