Second-rower James Bentley was sent off for a high tackle and substitute hooker Brad Dwyer sin-binned for a late hit during the 22-20 defeat.
Both are facing a possible ban and Leeds also lost Richie Myler - who was at stand-off - with a groin injury.
Winger David Fusitu’a took a knock to the head and didn’t feature in the second half and centre Harry Newman missed the game because of a hamstring strain.
Rhyse Martin played despite the sudden death of his father earlier this week, but the club are now arranging for him to travel to Australia to be with his family.
After the game, Myler admitted he was “sore” and Agar said: “It’s early days, but he wasn’t good enough to continue. We will have a fair few selection issues looking into next week.”
The coach had “no complaints” about the red card shown to debutant Bentley, but was mystified no action was taken against Warrington’s Ben Currie for a challenge on Fusitu’a.
“Ben Currie knocked David Fusitu’a out and we didn’t get a penalty,” Agar said.
Of Rhinos’ performance, Agar said: “It was a very tough loss.“The boys are hurting, I felt we dominated the game for large parts, with 12 men and with 11 men.
“Unfortunately, that caught up with us right at the death.
“I felt we definitely deserved something out of the game.
“I felt an awful lot went against us and our boys tried tremendously hard to ride it out.
“I am proud of the effort.”
Rhinos’ women beat Warrington 26-0 in a pre-season game played after the men’s match.
Try scorers were Sam Hulme, Zoe Hornby, Shannon Lacey, Orla McCallion and new signing Sophia Williams.
Tasha Gaines kicked three conversions.
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