So it seemed the Pittsburgh Penguins spent most of their energy antagonizing Kane instead of focusing on the Eastern Conference standings.
"We can't dwell on this," Crosby said. "That's not going to help anything. We have an opportunity a lot of other teams don't have."
The Thrashers also prevented Crosby from scoring his 50th goal of the season. The Penguins captain will have one more game -- Sunday at the New York Islanders -- to try to reach the milestone for the first time. Crosby, in his fifth NHL season, recorded three shots on goal.
He was more concerned that Pittsburgh, the defending Stanley Cup champion, finished behind the New Jersey Devils in the Atlantic. That cost the Penguins a chance for the No. 2 seed in the conference.
"It's disappointing," Crosby said. "We hoped to win and get second place. We'll have to play a good game [Sunday] and start focusing on the playoffs."
Atlanta, which has been eliminated from postseason contention, had lost five straight games. Little netted the only goal at 9:26 of the second period.
Pittsburgh had won eight straight over the Thrashers and was coming off a 4-2 homestand, but the Penguins appeared to lose focus after Crosby objected to a check into the boards by Kane midway through the first period. Crosby was penalized for cross-checking Kane at 10:24.
Kane was behind Pittsburgh's net over 4 minutes later when Michael Rupp was given a 10-minute misconduct and Eric Godard was called for roughing.
Penguins forward Matt Cooke skated off under his own power after a fight with Kane left him on his back for several minutes early in the second.
Cooke was the third of four Penguins skaters penalized for tangling with Kane, who appeared to anger the Penguins for hitting Crosby into the boards twice in the first period.
Cooke elbowed Kane 1:59 into the second. After both players took off their gloves near center ice, the 18-year-old Kane landed two hard right punches to Cooke's face.
"He challenged me and asked me to fight, and I was not going to back down," Kane said. "It's part of the game."
Medical personnel brought a stretcher onto the ice as the 31-year-old Cooke laid on his back, seemingly unable to sit up, but the 12-year NHL veteran soon insisted he was strong enough to skate off the ice and didn't return.
"He left the ice saying he was fine and he continues to be that way now," Penguins coach Dan Bylsma said. "He obviously will go through a battery of [concussion] tests."
Cooke, whose blindside hit of Marc Savard last month caused a concussion that likely ended the Boston center's season, wasn't sure when he will be able to return to the ice.
"It's a little sore," Cooke said. "We'll see how it is [Sunday]."
Atlanta coach John Anderson was disappointed that the Penguins played with a hard edge that could have injured Kane.
"If they take exception to who gets hit out there, does that mean you are supposed to start a fight?" Anderson said. "I don't get it. Crosby is so great for this game, but when you're always around the puck, you're going to get hit a little bit. Every time he gets body checked, does that mean somebody is going to get attacked?
"Cooke came at an 18-year-old. What goes around, comes around. That's all I can tell you."
Kane drew a slashing penalty from Penguins center Tyler Kennedy after Little scored from the bottom of the left circle.
Marc-Andre Fleury stopped 21 shots for Pittsburgh.
"We have to be better," Crosby said. "We have to make sure our game is where it needs to be going into the playoffs."
Thrashers C Jim Slater (lower body injury) left in the first period and didn't return. ... Penguins LW Alexei Ponikarovsky served the first of a two-game suspension for boarding Islanders forward Josh Bailey on Thursday. ... Pittsburgh LW Chris Kunitz (shoulder) was unable to play. ... Atlanta RW Nik Antropov (lower body) missed his second straight game. He is tied with Maxim Afinogenov for the team lead with 24 goals.