The national team beat the four-time champions 3-1 at Zayed Sports City Stadium in Abu Dhabi, the United Arab Emirates.
The two leaders also discussed bilateral relations and pledged to continue to further strengthen ties, presidential sources said.
Although the tournament was originally scheduled to be held in the summer, Federation Internationale de Football Association organizers switched it to November and December 2022 due to scorching weather.
Continental superpower Japan will be out to secure a record-extending fifth Asian Cup title when they take on a young Qatar side building towards the 2022 World Cup in what should be a tight final on Friday.
Team Qatar's stellar form and performances are all credited, according to one of the boys, to Sanchez' "high pressure and intensity, miserly defending and knowing when to kill the game at the right time".
"In claiming their maiden crown, Qatar have set the benchmark for all Asian teams and I am sure their success will serve as an inspiration for everyone to scale even greater heights", he added.
Qatar coach Felix Sanchez, however, said that he is not concerned by the reports.
But the tournament ended in heartbreak for Yoshida, who ironically conceded a VAR-assisted penalty that gifted Qatar their third goal and effectively ended Japan's resistance in the final.More news: Temperatures hit -15.4C as heavy snow hits the UK
The UAE, which lost to Qatar 4-0 in a politically-charged semifinal on Tuesday, questioned if two members of the Qatari team - 22-year-old Almoez Ali, a Sudan-born striker, and 21-year-old Bassam al-Rawi, a defender who is the son of a former Iraq global - meet FIFA's nationality requirements.
The glittering gold confetti that heralded Qatar's Asian Cup win had hardly fallen back to earth before the next challenge was being discussed.
During the semifinal between Qatar and the United Arab Emirates, some spectators threw footwear and plastic bottles on the field after the host UAE team went down to a 4-0 defeat.
In another interview, Sanchez shared his belief in the young players by saying that they "set a tune too hard for any of their rivals to match in the games".
"They were ready despite having only two days and played more aggressively than we did", Yoshida said.
The world can learn a lot from Japan, especially when it comes to cleanliness, courtesy and politeness. I'm very happy for the players and all the people in Qatar who supported us from the beginning.
South America is a different proposition and facing Colombia, Paraguay and Argentina will give a much better indicator of just how much work remains to be done for this Qatar side.