He praised his players’ determination and resilience, taking the Premier League side to the wire after a hard-fought 2-2 draw.
Caldwell acknowledged the disappointment of the defeat but highlighted the positives, believing the experience will benefit his squad moving forward.
He told ITV: "We showed what a special football club we are. I'm really proud of my players."
He added: "I am really proud of the team and the whole football club really. We showed what a special football club we are. We just came up short on penalties, which is a lottery. I am really proud of the players.
"We spoke a lot this week about team first and running for each other. I thought we were outstanding. With 10 men it was backs against the wall. We could have won or lost it near the end. It is a fantastic effort from the players.
"I think it shows the potential and what they are capable of and they can raise their game. We have to show that commitment to each other and if we do that, I am sure we have got a lot to look forward to.
"We are the only supporter-owned club in England and you can see the success we have had. There is a lot to look forward to at this club."