Redmond had the unenviable task of stepping up to the spot when England were down 4-3 in the shootout.
Unfortunately, Germany keeper Julain Pollersbeck saved his subsequent penalty relative ease.
The Southampton winger was visibly distraught after becoming the latest Englishman to falter in a shootout.
However, Everton keeper Pickford believes Redmond will learn from the experience.
"He's an experienced lad who has been at this tournament before so he'll move on and get better from that," said Pickford via The Mirror.
"Obviously there is a lot of support there for him but you can't crowd him after that. He's disappointed and on another day he'll score. He'll get better from that experience."
Redmond's Southampton teammate, Ward-Prowse, felt for his 'close friend' but held optimism that the 23-year old would be better off for the loss.
"It's difficult at the time. Nathan is a very close friend of mine and a team-mate at club level as well.
"It's important for him to learn from this experience. I know his mindset and I know this experience will make him stronger as a person and as a footballer. He is a good friend and he'll grow from this."