Honda, 32, came off the bench late in the last-16 clash with Roberto Martinez's side, but was unable to prevent his side from slipping to an agonising 3-2 loss.
"Today we showed how we can proceed as Japanese football," the former AC Milan midfielder told reporters after the match.
"I might have finished my career for the national team, but I'm happy because we have many young players following us, and I think that they will make new history for Japanese football."
Japan held a two-goal lead in the 52nd minute following strikes from Genki Haraguchi and Takashi Inui, but Jan Vertonghen and Marouane Fellaini levelled the scores before Nacer Chadli’s injury time goal secured a dramatic win for Belgium.
"This is the last World Cup for me," Honda added. "That’s the reality. To be perfectly honest, I wanted to take everyone to the next round but I couldn’t get the job done. I did everything I could. I did the best I could.
"Belgium deserved the win, but we also played as well as we possibly could. I just want to thank my team mates."
Honda, who scored 37 times in 98 appearances for his country, was used as an impact player off the bench in his third World Cup and had a couple of chances to grab a winner for Japan before the dramatic denouement.
"We had talked about the score being even if and when I entered the game, but I couldn't come through," said Honda.
"I've always said if you're in this competition you should be in to win it, and I hope the younger generation of players carry on that spirit."
Hasebe, once heralded by former Japan head coach Alberto Zaccheroni as one of only two "true captains" he had ever managed along with Paolo Maldini, has also decided to step down from international duties.
The midfielder, who plays in Germany for Eintracht Frankfurt, made 114 caps for Japan.
"I would like to express my gratitude to my colleagues who fought together for about 12 and a half years since 2006, and to all the Japanese people who supported me so much," the captain said in a post on Instagram.
"The time I walked with you is an important treasure for me. Thank you from the bottom of my heart!," he added.
"Last but not least, I am also a supporter of the national team. Let's dream about the Japanese national team together."
Japan's squad was one of the oldest at Russia 2018, with an average age of over 28.
With the majority of the squad set to be over 30 years old for the next World Cup in 2022, a new generation will need to pick up the mantle left by the likes of Honda and Hasebe.