We don't even know what the Jays final offer was. You need to remember that the Cards also could offer him the chance to stay in CF. The Jays very well could have been offering a similar or even greater deal in the end, and he simply chose St Louis - we can't blame Rogers or our management for that.
You have to analyze what a guy is worth to the team, and set a limit on what you're willing to spend. If he simply wants to be somewhere else (and for a perfectly fair reason), you can't just keep throwing money and/or term at him until he changes his mind.