Kasprowicz took 0-15 and 7-39 while leg spinner Warne took 3-20 and 0-61 in Darwin as Australia clinched a 149-run win inside three days.
Warne has 520 career wickets, seven short of Sri Lanka off spinner Muttiah Muralitharan's world mark.
The 32-year-old Muralitharan has withdrawn from the two-match series for personal reasons.
Warne said this week he felt an eight-wicket haul in Cairns in the second Test starting on Friday may be beyond him, given the pitch is expected to suit fast bowling.
"Ha ha. No, not at all (was Warne unhappy). I think that's the beauty of this team," Kasprowicz told reporters in Cairns on Wednesday.
"Everyone is out there playing for one another just to get the job done," the 32-year-old Queenslander added.
"I know Shane's pretty keen to get that record. Ultimately it's all about the team and winning the series."
However, Kasprowicz said all the Australian players would love to help Warne set a world record before Muralitharan returns to action later this year and continues taking big hauls of wickets.
"Being part of the team that's involved in history is important to everyone in the team," Kasprowicz said.
"Being involved in a game where Shane Warne got a record would be something that everyone would certainly remember."
Kasprowicz said the Australians would be trying to avoid the trap of bowling too short on a bouncy wicket, but would still be sending down plenty of short stuff to test the touring team's batting line-up.
"The Sri Lankans are used to wickets playing a bit lower," the tall right-armer said.
"Our bowlers are blessed with a bit more height than theirs. If there is going to be some bounce there, we'll probably find it."
