The Three Lions exited the competition at the group stage for the first time since 1958 after losing their first two matches.
Henderson believes that the Three Lions should look ahead to the future after their early exit in Brazil.
"Everyone is disappointed. We're really down because we are going home far too early," he told the FA's official website.
"It's not a great mood [around the camp], but it's a time everyone needs to stick together, everyone needs to stay strong.
"I'm sure there will be days when you'll wake up and it'll come back into your head, but at the same time, what doesn't kill you makes you stronger and you have to keep going."
England face Costa Rica in their final match in Group D on Tuesday.