The 31-14 defeat has dented their promising start to the campaign.
They beat the Crusaders in the opening round and put up a strong effort against the Chiefs in round two.
But the Highlanders (five points) have slipped to eighth place following the loss to the Reds, and Joseph was frustrated their efforts at home did not translate to a better result in Brisbane.
He was left ruing their inability to score points when in control during the opening 20 minutes.
"The fact we’ve only won four times here in 30 years tells you something," he said.
"It’s not just this year, last year, year before ... the Highlanders have really struggled here.
"But we’ve had a good week, trying to get our minds right for a big match.
"The Reds, they really took it to us, good luck to them."
The Highlanders’ kicking game was inconsistent at times, and they missed 31 tackles, which is a significant number.
Hard-working openside flanker Sean Withy missed five, which was out of character.
The Reds (five points, sixth place) also missed their share of tackles. Highlanders second five Timoci Tavatavanawai busted nine tackles, which is really impressive at the Super Rugby level.
The Brumbies snatched a late 30-27 win over the Blues (five points, fifth) in Canberra and lead the competition standings with 14 points from three games.
No 8 Charlie Cale scooped up the ball from the back of a ruck and crashed over in injury time to secure the win.
The Fijian Drua (four points, 11th) recorded a 25-20 win over the Hurricanes (six points, fourth) in heavy rain in Lautoka.
The Hurricanes led 17-13 at halftime but struggled in the conditions and let the game slip away.
Their first five Brett Cameron will miss the remainder of the season.
He will undergo surgery after sustaining a knee injury during the round two match against Moana Pasifika.
"It’s obviously hugely disappointing to lose one of our best players,” Hurricanes coach Clark Laidlaw said.
"We’re here to support and help him through it, initially with the surgery and then with the rehab.
"We know it’s a tough road ahead, but we also know that he’s up for it and we’re up for it to support and rehab him so he can get back to playing as soon as possible."
The Crusaders (five points, seventh) bounced back from consecutive losses to beat the Chiefs (eight points, third) 43-33 in Hamilton.
Otago No 8 Christian Lio-Willie scored three tries to help the defending champions build a 43-21 lead.
The Chiefs rallied late, but the game was already lost.
The Force (four points, ninth) ran in five tries to beat Moana Pasifika (four points, 11th) 35-19 in Pukekohe.
