Hamilton signed a five-year, $125 million deal this offseason with the division-rival Los Angeles Angels and recently stirred the passions of Rangers fans by saying the Dallas-Fort Worth area isn't really a baseball town.
"You just don't replace a talent like that, and we all know that," Ryan said Friday as he arrived at spring training in time for the club's first Cactus League game. "But also, there's a dimension that's brought to the ballclub that very few players, if any other player in baseball, would bring. It's so unique and unusual that you can't put other players in that category."
Ryan added that Hamilton was a critical component to a team that won the AL pennant in 2010 and 2011.
"Josh had a big impact on our organization, and we wouldn't have gone to two World Series without him," Ryan said.
Ryan said that the day Hamilton signed with the Angels was a tough one for the organization.
"I think the 'pucker factor' went up considerably," he said.
"I think that we stepped back, assessed the situation and were able to accomplish some things that needed to be done as far as strengthening our ballclub," Ryan said. "I think we're a better ballclub today than we were the day Josh signed with the Angels. That's the way I look at it.
"Now, would I have liked to have added a starter to the rotation that was experienced and consistent, keep you in games? Yeah, I would. And you would have liked to have been able to bring a veteran bullpen guy. But we hustled around, we brought some people in, but obviously they have to step up and do the job."
As for Hamilton's recent comments about Rangers fans, Ryan shrugged.
"Josh is probably making an adjustment mentally and emotionally to new surroundings and being with another ballclub and with the way the season ended last year," Ryan said.
He said he expects his team to learn from how the 2012 season ended, as the Rangers blew a five-game lead with nine to play, losing the AL West to the Oakland A's.
"We didn't play well down the stretch," Ryan said. "I think emotionally we were drained as a club, physically we were drained as a club. I think with the history of our ballclub the two previous years, our expectation was they were going to get it together and play at a level we felt like they were capable of playing, and it just didn't happen."
Ryan admitted that he was "somewhat guarded" in regards to his overall feeling as Cactus League games begin.
"We feel like we have a good ballclub, but we also know people are going to have to play to their abilities and they're going to have to stay healthy," Ryan said.