Italy, which did not qualify for the 2018 World Cup, missed out on soccer's global showpiece again after they suffered a 1-0 defeat at home to North Macedonia in Thursday's playoff semi-final.
Since lifting their fourth World Cup trophy in 2006, Italy have not played a knockout game in the World Cup, having only won one group stage match at the finals in that time.
"I hope Mancini continues with us," Gravina said.
"He has a commitment with us for this project. I hope he can shake off this elimination just like all the Italians and that he remains at the helm to continue our work together."
The Azzurri were feted as national heroes after they won the European Championship in July 2021 but the team have crashed back to earth after missing out on the World Cup finals for the second time running.
"Just as we accepted the praise last summer, we must accept the criticism coming our way, but I must try to protect this national team," Gravina added.
"We go forward with heads held high. We must not lose the enthusiasm of last summer... Criticism is fine, but we don't want the risk of doing even more damage."
