Italian Football Federation president Gabriele Gravina said he would like Mancini to remain as coach, but an official announcement has yet to be made.
"I talked to Gravina; we are aligned on everything," Mancini said in a news conference on Monday. "Let's think about this match, then calmly we will think about everything, to understand what to improve in the future."
After finishing second in their World Cup qualifying group to Switzerland, Italy slipped to a shock defeat in their playoff semifinal and missed out on World Cup qualification for the second time in a row.
In July, Mancini led Italy to Euro 2020 glory while also guiding the side to a world record 37-game unbeaten run, which ended in October with a 2-1 loss against Spain in the UEFA Nations League semifinal.
"There are important national teams that have not won anything for 60 years," Mancini added ahead of Tuesday's game at Turkey. "Italy is a little further ahead in this, despite some disappointments. Sometimes we exaggerate saying that we must necessarily look for the reasons.
"Despite the great disappointment of Palermo, I am pleased that the work done in these three years has been appreciated. It's not just the European Championship, these players must also be given credit for the long streak of matches without defeat.
"We don't just have good players; these are special guys who have created an exceptional group. Not only in the locker room, also everything around [Italy's headquarters in] Coverciano, in the Federation, here there is a perfect group that seemed ideal for me to achieve success."
Mancini also said Italy shouldn't have been in the position to qualify for the 2022 tournament through the playoffs.
"We should have won our group with at least a two-point advantage over Switzerland," he added. "I don't want to find excuses for what's happened, we have to accept reality and move on."
Mancini added that he accepts that certain changes are required for Italy to move forward: "We have to start over, start thinking differently. We will include younger players in the national team, in the hope that they will have more opportunities in their respective clubs as well. We will start from this, then we will see what to do in a more general context."
Italy defender Leonardo Bonucci also said the team are united and determined to put things right.
"As for me, I want to continue to be a guide for young people in the national team," he said on Monday. "The 48 hours after the elimination were tough. We played it down, the coach put a full stop on the past and we have moved on. Now we have to start again to rebuild what we were unable to achieve. The foundations are there."