In fact, team president Randy Levine said he feels bad for the five-time All-Star second baseman, who this week finalized a 10-year, $240 million deal with the Seattle Mariners.
Asked if he was disappointed that Cano reacted the way he did at a news conference in Seattle on Thursday, Levine said, "No, I feel bad for him because I think he's disappointed he's not a Yankee. But I respect him, and he's free to say whatever he wants to say. We still respect him, and he'll always be fondly remembered as a Yankee."
Levine said Cano's age -- he turned 31 in October -- precluded the team from giving him the kind of long-term deal that backfired with Alex Rodriguez and could do the same in the cases of CC Sabathia and Mark Teixeira.
Later Friday, MLB spokesman Pat Courtney told multiple Los Angeles media outlets that the league would be investigating the Yankees for tampering after Levine dropped Trout's name.
Team officials are prohibited from talking about players under contract to other teams. Trout is not eligible for free agency until after the 2017 season.
General manager Brian Cashman said Cano's agent, Brodie Van Wagenen, offered the Yankees a minor discount -- 10 years at $235 million -- but that the team had no intention of breaking its vow not to give Cano a 10-year contract.
"Sometimes the business of baseball can create some hard emotions, I guess, but we loved Robbie and he's a great player," Cashman said. "At the same time, business is business. Everybody has to make tough decisions, and sometimes those decisions can feel personal, but there's nothing personal about it.
"We made an offer that we were comfortable with making, and it fell far short of where Seattle was. In terms of respect, they showed a lot more respect financially than we did."
Cashman said he had nothing but fond thoughts about Cano's time with the Yankees.
"Bouquets, bouquets, bouquets," he said. "I'll throw him bouquets all he wants, but I couldn't throw him $235 million."
Owner Hal Steinbrenner said he was not angry but allowed that he was surprised by Cano's choice of words Thursday. Steinbrenner disagreed that the Yankees' offer was a show of disrespect to the best hitter in their lineup last season.
"I don't take it that personal," Steinbrenner said. "There was nothing disrespectful about the last offer that was on the table, which was $25 million for seven [years, annually]. I'm not quite sure why he feels that way, but it is what it is."
Levine, Cashman and Steinbrenner addressed Cano's remarks during a Yankee Stadium news conference to introduce Jacoby Ellsbury, who apparently felt quite respected by the seven-year, $153 million contract he signed with the Yankees.
"From the get-go, the Yankees showed a great interest in me, that they really wanted me," said Ellsbury, a member of the 2007 and '13 World Series champion Boston Red Sox. "It was a very easy decision once they made it very clear how much they wanted me, not only for now but for the future."