The manager put Monday night's narrow defeat at Goodison Park down to a lack of potency in the final third, as Everton edged the Premier League contest by a single goal.
Richarlison had the hosts ahead inside nine minutes, but Southampton weren't without their own chances in the second period, with opportunities falling to Moussa Djenepo and Jannik Vestergaard late on.
Accepting that his side are low on self-belief, Hasenhüttl did pick out the performance of Stuart Armstrong as a positive to take away from an otherwise frustrating evening, as the Scot deputised manfully in the absence of Oriol Romeu - whose season has been ended by injury.
Speaking about the midfielder, he said: "Stu showed me tonight that I can trust him in that position, he played a good game. That was a positive. Ori [Romeu] is out now until the end of the season. We have a lack of punch in the final third, this is what we know. It's not surprising.
"One goal is the difference. We lost again because we're short of scoring goals in the moment, and then it's difficult to win games.
"For the situation we're in at the moment, with Stu [Armstrong] as a six and Moussa [Djenepo] as a right-back and so on, it's very tough."
Commenting on the inclusion of Fraser Forster in the Saints XI, he added: "We tried to bring some momentum in our game with him. He made a good job in the cup and deserved to get a chance. It was okay.
"Nathan Tella came in today, tried some things. Three Academy players at the end. What can I say? This is what we have at the moment. We have to make the best of it, that has to be our goal.
"We are not full of self-confidence. I don't want to overload the players with the expectations I have; I know that we cannot play like we did at the start [of the season]."