Parker, already aware of Joshua's power, saw more examples of it this morning, particularly when Joshua attacked in flurries. Klitschko, hurt by a right uppercut in the 11th round, went down, and then down again after a Joshua onslaught. A third on the ropes prompted American referee David Fields to stop the fight.
But Parker also saw vulnerabilities, particularly Joshua's habit of throwing only one punch at a time and standing square on, waiting for a reply.
Parker said: "I want to get in the ring. When you're watching, you want to fight too. Kev and I were excited about it and were picturing combos that we could land on both of them."
He later sent a congratulatory message to Joshua on social media.
Barry said: "Joe's movement will give him [Joshua] fits. Joshua, one punch at a time, oh my goodness. He was there to be hit by Klitschko.
"As a coach I envisaged Joe doing what he is good at and him landing against both guys."
Both thought Joshua, gassed from his attack in the fifth round and knocked down in the sixth with a beautiful right hand from Klitschko, was there for the taking.
"He did look completely gone, and I think ... Klitschko will be very disappointed because the next two rounds I believe Anthony Joshua was a like a dead man walking," Barry said.
"Klitschko let him off the hook, he let him walk around and recover and I remember saying to Joe, 'if he gets past the seventh round this could change things around'.
"I think the fight was there for Klitschko to win, but great character from Joshua. He showed he's still a young guy and still developing - it was a huge step up in class for him and he came away victorious. When you let your hands go you increase your chances of winning."
Klitschko was extremely gracious afterwards, saying Joshua was too good on the day. Far from a spent force, he looked fit and full of movement and attacking instincts, and his defensive class was obvious. But in the end Joshua's power was too much.
Barry, who oversaw two sparring sessions between Parker and Klitschko in Florida in 2014, said: "He was fighting for his legacy. He must have thought, 'ok, this is all or nothing'. He looked terrific out there. I'm surprised by how good he looked."