Samurai Blue beat both Germany and Spain in the group stage of the tournament to make the first knockout round, where they were drawn to play Croatia.
Japan took the lead in Monday's contest through Daizen Maeda, but Ivan Perisic levelled the scores early in the second period, and Croatia went on to win 3-1 on penalties to advance to the final eight of the World Cup.
Moriyasu has denied that his side "succumbed to pressure" in the shootout despite missing three of their four penalties through Takumi Minamino, Kaoru Mitoma and Maya Yoshida.
"The players showed us the future, a new era of Japanese football. We beat Germany, we beat Spain... If we take confidence in that, and if we think about overtaking these teams rather than just catching up, the future is bright," he told reporters.
"I don't think they succumbed to pressure. The players who played the 120 minutes and those who took the penalties were courageous. I would like to praise their efforts, they tried under such immense pressure.
"Of course, we wanted to win and the result is unfortunate, but it does not negate all the efforts of the players. We couldn't break the barrier towards the final eight, but the players were able to show a new generation of Japanese soccer."
Arsenal defender Takehiro Tomiyasu has also revealed his disappointment with the result and claimed that his own performance against Croatia "was a disaster".
"It was not enough and also for the team, we did not deserve to win. We were so close to achieving our aim. They were better than us. I can't be proud. I am not satisfied about what happened. This is football and we need to be much, much better to win against a stronger team," he told reporters.
"Of course, we are so disappointed with the result. My performance was a disaster today so I am sorry for the team. I just need to be much, much better to help the team."
Japan have still never progressed to the quarter-finals of a World Cup, with three of their last four participations in the tournament coming to an end in the round of 16.
Takuma Asano was the only Japan player to score in Monday's penalty shootout, but Croatia converted three of their four spot kicks to advance to the next round.