Williams was slapped with a four-week ban for his no arm tackle on Anthony Watson of the Lions in 2017.
"For me I have a clear picture on the field," Garces told the television match official following the Barrett incident on Hooper.
"He never uses his arm. He just puts his shoulder and elbow on the neck and head so it's clearly dangerous. It's direct with force so I have no option but to be a red card against four," he added.
The All Blacks lost the test by a record margin - 47-26.
The SANZAAR Foul Play Review Committee of Adam Casselden SC (Chairman), Stefan Terblanche and Eroni Clarke assessed the case on Sunday night.
In his finding, Foul Play Review Committee Chairman Adam Casselden SC ruled the following:
"Having conducted a detailed review of all the available evidence, including all camera angles and additional evidence, including submissions from his legal representative, Stephen Cottrell, the Foul Play Review Committee upheld the Red Card under Law 9.16."
"With respect to sanction the Foul Play Review Committee deemed the act of foul play merited a mid-range entry point of 6 weeks due to World Rugby instructions that dictate any incident of foul play which results in contact with the head and/or neck must start at a mid-range level. However, taking into account mitigating factors including the Player's exemplary judicial record, his expressed remorse and the fact the Player has pleaded guilty at the first available opportunity, the Foul Play Review Committee reduced the suspension to 3 weeks."
"The Foul Play Review Committee adjourned the hearing to seek more evidence regarding the Player's proposed schedule of matches. Upon reconvening the Foul Play Review Committee was presented with extensive evidence demonstrating the Player's intended playing schedule."
"The player is therefore suspended for 3 weeks, up to and including Sunday 1 September 2019."