"I know there are no guarantees of winning and the only thing we have is to work on chances".
He said: "At 3-0 maybe we drop a little bit in our concentration I think we start to think the game was over and always it is so risky when there is so much time to play".
He will lead the Saints for the first time as they travel to Cardiff on Saturday, looking for the win that would take them out of the relegation zone.
"Of course in the end, Lloris was man of the match because it was an unbelievable action that save, but that we can not afford".
'I can't guarantee you how many results we will earn for that.
Hasenhuttl might decide to focus on the backline in his first training session following this dismal defensive display at Wembley. Danish midfielder Pierre-Emile Hojbjerg saw one stunning effort pushed on to the post by Lloris before Nathan Redmond saw his deflected shot come off the bar.
"When they their push their limits we will see where they get".
Cardiff, in contrast to their relegation rivals, are now up to 14th courtesy of four wins in their past five home fixtures.
"This managerial change offers us a fresh start and, very quickly, Ralph emerged as our ideal candidate".
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.
Hasenhuttl may wish he had stayed away on Wednesday, as Southampton turned in the kind of error-strewn display that has blighted their season so far, conceding three soft goals and committing too many sloppy mistakes.
Last season under Hasenhuttl, Leipzig played in the Champions League for the first time and subsequently reached the Europa League quarter-finals.
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).