Ryan's move to Hamilton was announced on Wednesday after he was seen by Chiefs coach Clayton McMillan when he was involved with the Barbarians' game against the New Zealand XV in London last month.
Ryan, who had been part of the Wasps club that went into administration, signed a short-term contract with Munster in October.
Former Ireland and British & Irish Lions lock Donal Lenihan told Irish radio's podcast that poor planning and management of Ryan by Munster left them in a vulnerable position.
"The thing that annoys me in the business around John Ryan is that he should never have been let go in the first place. [He was released by Munster at the end of the 2021-22 season].
"If you don't have a scrum in Europe, you've nothing, and with the South African teams coming into the United Rugby Championship, it has an effect there as well," he said.
Lenihan said as soon as Ryan became available, Munster should have tied him up for the season, not just on a three-month contract.
"Because he had a three-month contract, and I don't know this for certain, but I would imagine, he had already agreed to play for the Barbarians in those games against the All Blacks XV, because he wanted that to put him in the shop window."
Ryan then played with some New Zealand players with the Barbarians around the same time it was realised Angus Ta'avao would be out of action for 12 months for the Chiefs.
Lenihan said, "So, all of a sudden when the Chiefs need a tighthead prop, somebody came up, 'oh jeez, your man John Ryan, who is available, is really impressive."
He said that if Munster had him on a 12-month contract, he wouldn't have been available to the Chiefs, and if they had not agreed to let him play for the Barbarians, the issue would not have come up.
"Munster are the architects of their own downfall in this," he said.