Crosby failed to shake the hand of all the Detroit players, including Red Wings' captain Lidstrom, after Pittsburgh won the Stanley Cup at Detroit's Joe Louis Arena on Friday night after a 2-1 win in Game 7 of the finals.
"I think that's one thing you should do," Zetterberg said as the Red Wings cleaned out their lockers for the summer on Monday. "I don't know why he didn't do it, it's disrespectful."
Crosby said he was celebrating with his teammates, but did not apologize for not upholding the NHL playoff tradition of the captain leading his team in a line to shake hands with the opposing team.
Lidstrom, along with a few other players -- including Kris Draper -- waited for Crosby, but finally left the ice after a period of time.
"You know you're happy and celebrating with your teammates," Lidstrom said. "But you know the losing team wants to get off the ice too. ... Sidney was probably caught up in the emotions and everything."
Lidstrom added Crosby would learn from the situation.
The pair will likely cross paths again on Thursday at the NHL awards ceremonies in Las Vegas. Lidstrom is a finalist to win his seventh Norris Trophy.
Lidstrom missed the final two games of the Western Conference finals because he was speared in the testicle by the Chicago Blackhawks' Patrick Sharp in Game 3 and had to undergo surgery. But he returned for the opening game of the Stanley Cup final.
The biggest offseason issue for Detroit will be whether or not to keep free agent right wing Marian Hossa.
Hossa, who scored 40 goals during the regular season, left the Penguins in July -- spurning a multiyear deal -- to sign a one-year contract with Detroit because he thought the Red Wings gave him the best chance to win the Stanley Cup.
He had six goals total in the playoffs and only three assists in the Stanley Cup finals and had to watch his former team hoist the Cup.
He says he wants to stay in Detroit, but there's also salary cap restrictions.
"Detroit is No. 1 on my list ... I had a great time in here with these people and I don't regret anything," Hossa said. "My agent Ritch (Winter) and Kenny (Red Wings' general manager Ken Holland) will sit down and talk about some stuff."
Hossa says he wants a long-term deal. Detroit signed Zetterberg and Johan Franzen to 12- and 11-year extensions, respectively, during the regular season.
Detroit isn't expected to bring back 47-year-old defenseman Chris Chelios, who didn't speak to reporters on Monday. Chelios has said he wants to continue playing.