Saints looked on course for a first victory in five Premier League games following a fine strike from Nathan Redmond.
But the south coast club have made a habit of dropping points from winning positions and were once again pegged back when a glaring error from goalkeeper Angus Gunn was punished by Alex Pritchard.
Manager Hasenhuttl, who replaced the sacked Mark Hughes in December, felt the match encapsulated his time at St Mary's and believes there is plenty to work on during the summer.
"To lose (points) where the opponent doesn't really have a goal chance – we had a lot of them – hurts really," said the Austrian, whose team finished 16th.
"It's a little bit like a picture from this season. It's exactly what we know we have to change next season, that's for sure.
"If you play an intense way, an aggressive way, we are good, we can score, we can create chances.
"If you are a little bit sloppy, every mistake is immediately a goal and that's something we have to change next season.
"It is a clear message for the team, it is a clear message for me.
"Next season – maybe with a few new players also – (we need to) create a new spirit, a new mentality because it must give a different picture from the first game day.
"It's too easy how we gave the points away, especially today again. If we stop this, and we have to, then we will take more points. That has to be our goal next season."
After Redmond's stunning 41st-minute strike from just outside the D, James Ward-Prowse saw a thumping 25-yard effort touched on to the crossbar by Terriers keeper Joel Coleman early in the second period.
England Under-21 international Gunn then paid for a momentary lapse in concentration as Pritchard nipped in to score for the first time since November.
Speaking about Gunn, Hasenhuttl said: "I think he knows that he still has to work on his game.
"He made a few fantastic games but he hasn't reached his limits.
"He has to improve his game and he has a lot of weaknesses he can work on."
For Huddersfield, the draw resulted in their first away point since January and prevented the club equalling the record for Premier League defeats in a season.
Terriers manager Jan Siewert wants to bring stability back to the Yorkshire club as he prepares for the Sky Bet Championship.
"I was really pleased with the performance at the end and this builds momentum for us after a tough game against Manchester United (also a 1-1 draw)," said the German.
"After such a season, you have to talk about all the things in detail.
"For me, it's important to be stable and prepare well for our Championship season.
"We are all ambitious but important for me first is to have a stable spine to the team."
Huddersfield turned the away end luminous yellow by handing out free shirts to all travelling fans as a reward for their support during a challenging campaign.
Speaking about the Town supporters, Siewert said: "You should make a story just about them this season because they were amazing.
"They are the petrol for us. Big, big credit to them. They were impressive."