The 35-17 win was secured with four tries from his much-vaunted backline as well as a match-turning penalty try, but Joseph felt the way his forwards matched the physicality of the international-laden Waratahs pack had been key to the victory.
"They aren't All Blacks, they aren't Wallabies, they aren't Springboks but they are very good rugby players," the former New Zealand flanker told reporters.
"And I guess you can see that we've created a very good team. Yeah, we've got a very good backline but I think in the last three or four games the pack's really stood up and at crucial times of the season they've done that."
The reward for the victory over the reigning champions is a trip to Wellington next Saturday to take on the Hurricanes, who have been the best side in the competition this year.
It will be a second final for the Highlanders and ensures a first-time champion for Super Rugby, but Joseph felt his team would still be very much the underdogs.
"It still surprises me, in many ways it seems that we've fooled the rugby community, they still don't quite believe in us, what else can these guys do?" he said.
"But the Hurricanes are stacked with All Blacks, they're in form, they've only lost a couple of games. It's a big task and we've got to play it up there as well. It's as big a task as this one was tonight."
Captain Ben Smith felt the match against the Waratahs turned on referee Craig Joubert's decision to award the penalty try in the 58th minute, when Patrick Osborne was prevented from getting the ball over the line by Jacques Potgieter's swinging arm.
That gave the Highlanders a 27-17 lead and an extra man for 10 minutes while the South African flanker sat in the sin-bin.
"The penalty try swung the momentum our way and we got a lot out of that," Smith said.
"There's always going to be chances in a game where you can get the momentum and that penalty try definitely did it for us, the boys were pretty excited by that."
