"When did it become OK for someone to hit home runs and forget how to play the rest of the game?" he asked.
Speaking about former Cubs teammate Andre Dawson, Sandberg said that "he's the best I've ever seen.
"He did it the right way, the natural way, and I hope he will stand up here [on the stage at Cooperstown] someday," Sandberg added.
Concluding what some observers called one of the most poignant acceptance speeches in recent history, Sandberg said that because of his respect for the game and getting the most out of his ability, "That's why I stand here today.
"I hope others in the future will know this feeling for the same reason: Respect for the game of baseball. When we all played, it was mandatory. It's something I hope we will one day see again," he said.
During an interview session after the ceremony, Sandberg explained that he wasn't trying to single out one particular player or one particular incident in developing his thesis.
"I watch these games and you see players self-promoting," he said. "You see a lot of that. They hit a home run and their team is still down four or five runs, and here they are tipping their cap to the camera because they hit a home run. That drives me nuts. I say, hit a game-winning home run and circle the bases. Now tip your cap. That was my style and that's what I would like to see more of -- a team concept of 'we,' not 'I.'"
During the speech, Sandberg played to the Cubs fans, many of whom were in attendance among the 28,000, waving blue hats, placards, pennants and banners. In thanking them, Sandberg said he felt like he was playing a "home game," adding that his one regret was that he never brought that World Series to Chicago. The Cubs haven't played in one since 1945 and haven't won one since 1908.
To punctuate that point, Sandberg told a joke about a man who asks a genie to bring peace to the Palestinians and Israelis by showing him a map of the Middle East. When the genie says he can't solve the problem, he asks the man for a backup wish.
"The guy says, 'Well, I always wanted to see the Cubs in the World Series,'" Sandberg said. "The genie looks at him, reaches out and says, 'Let me have another look at that map.'"
Sandberg also thanked the Baseball Writers Association of America for electing him to the Hall in his third year on the ballot. In doing so, Sandberg joked about how bad a quote he was during his playing days.
"I think a large part of [my election] is the fact that I was a great interview and gave you so many quotes you could wrap a story around," he said. "Seriously, I know I wasn't the best interview for many of those years, but I wasn't trying to be difficult. I had other things on my mind. Baseball wasn't easy for me."
Sandberg evidently saved the best for last. He said he wrote his own speech and put plenty of thought into it during the seven months since he received the call that he had been elected to the Hall this year with five-time American League batting champion Wade Boggs.
During the speech, Sandberg said he didn't play the game right because he "saw a reward at the end of the tunnel."
"I played it right because that's what you're supposed to do -- play it right and with respect."
He said people like late Cubs announcer Harry Caray and former Cubs manager Don Zimmer compared him to Jackie Robinson, the Hall of Fame second baseman who shattered baseball's color line in 1947.
"Can you think of a better tribute than that?" he asked. "Harry, who was a huge supporter of mine, used to say how nice it was that a guy can hit 40 homers or steal 50 bases and drive in 100 runs, but was also the best bunter on the team. 'Nice?' That was my job."
He called the induction and speech his last big game, his last big at-bat, his time catching the final out.
"I dreamed of this as a child, but I had too much respect for baseball to think this was ever possible," he said. "I believe it [happened] because I had so much respect for the game and respect for getting the most out of my ability."