Denmark lost 3-2 in the shoot-out after a 1-1 draw in Nizhny Novgorod, Schmeichel having denied Milan Badelj and Josip Pivaric before Ivan Rakitic rolled in the decisive spot-kick.
Schmeichel also saved Luka Modric's penalty deep into extra-time, Denmark's Mathias Jorgensen having been penalised for bringing down Ante Rebic as he shaped to convert an open goal having rounded the goalkeeper.
Leicester City's Schmeichel protested that decision to match official Nestor Pitana, claiming Jorgensen - who opened the scoring in the first minute - had won the ball in making his desperate lunge for the ball.
And Schmeichel indicated Pitana's calls were not fair during the contest, which saw Croatia move into a quarter-final against hosts Russia in Sochi.
"It's a strange feeling. Huge disappointment but also enormous pride about our team - not only the 11 on the pitch but everyone involved with the team," Schmeichel told a news conference.
"We had the opportunity, I think we were the better team in the second half and in extra-time.
"We had no luck, I don't think the referee liked us. It is difficult to accept and put into words. There are so many emotions right now.
"I don't feel let down by my team-mates – anybody who is brave enough to take one [a penalty] is a hero. If you have the balls to take on you have my utmost respect.
"We win and lose as a team. This is a fantastic team that I'm proud to be part of. We'll be back. We must remember this feeling now and use this in future.
Schmeichel indicated he works on saving penalties in training but opted to go with his gut during the Croatia clash.
"I've played a lot of games and today I went with my intuition. Unfortunately it was not enough in the end," the goalkeeper added.
"You can never replicate the pressure you're under in a game. Pressure does things to people.
"You can train all you want but when the pressure's on it's a tough situation and anyone who has the nerve to step up and take one has my utmost respect."