They lost 28-24 at Leeds Rhinos on Thursday night, meaning the club that finished third last term have now suffered defeat in all three of their opening Super League games, their worst start since 2007.
Slovenly Huddersfield were 18-0 down inside just 25 minutes yet mounted a stirring comeback so that, when Brett Ferres scored in the 68th minute, they took the lead for the first time at 24-22.
However, another momentary lapse in concentration gifted Paul Aiton a try with six minutes to go, meaning Leeds could pick up a first home win against their West Yorkshire rivals in five years.
“We did well to come from 18-0 down to getting within touching distance of a win,” said ex-England hooker Lunt.
“I don’t think it was anything to do with us (the start); Leeds came out and they played really well so all credit to them. We didn’t do too much wrong.
“We completed 16 out of 18 sets in the first half so it just shows you how well they have played.
“We got over that little arm-wrestle and got back in the game but it just shows what a quality side Leeds are.
“You just can’t be as ill-disciplined as we were. That’s what cost us at the end of the game.”
Lunt, who won the 2012 Grand Final with Leeds while on a season-long loan from Huddersfield, added: “You do think you can push on to win when you get in positions like we did after Brett’s try.
“But you can never write a team like Leeds off as they have so many good players who can do off-the-cuff things and score out of nothing.
“And it was that ill-discipline that hurt us.”
After a disappointing 19-0 home loss to Hull FC was followed by a better display in defeat at Wigan, he does believes improvements are there and, hopefully, that first win will come when Widnes Vikings visit them on Friday.
Lunt, 28, said: “We’ve been getting better each week so that is a positive for us. We just need to put an 80-minute performance together and get that win.”