Despite having Zane Tetevano sent-off just after the break, Leeds trailed by only two points until Saints sealed their place in the fourth round with a last-gasp converted try.
Rhinos were without 12 senior players, had forwards Rhyse Martin and Cameron Smith as their half-backs and gave a debut to 17-year-old substitute Morgan Gannon.
Having trailed 20-6 on the hour, a brace of tries by Brad Dwyer got them back into the game and Agar said he was “proud of the performance from start to finish”.
He reflected: “Obviously we had some very difficult circumstances with our team selection, with injuries.
“I have been in the game a long time and had really bad injury situations before, but I don’t think I’ve ever had one where every spine player and most of your backs are ruled out.
“We had a lot of forwards to pick from and we clearly had to adapt our game and try and come up with a game plan we felt would suit our personnel and could rattle Saints a bit.
“I thought they delivered it to a tee.
“We knew we had to keep the scores close and chances would be hard to come by, but we came within a whisker of doing it.
“We don’t want to be gallant losers, but I think there’s enough in there to suggest this team - and particularly some of our young players - have really got something in us.”
Agar didn’t make an issue of Tetevano’s dismissal.
“I’ll have a look at it, but we can’t do anything about it now,” he said.
Fijian forward King Vuniyayawa made his debut off the bench, but lasted only three minutes before being concussed.
Agar said: “He’s okay, clearly - getting knocked out - he wasn’t in a fit state to come back on, but he’s up and talking and he’s fine.”