Sanogo signed for the Eredivisie side on a season-long loan deal in July and scored a hat-trick in his first start for the club on Monday as they beat Qatari side Umm Salal 6-1 in a behind-closed-doors friendly.
Yet De Boer, whose twin brother, Frank, is in charge of Ajax's senior team, expressed his doubts over the France Under-21s international's value to the club.
"I heard Frank say last week that this is one of the best squads with whom he has ever worked," he wrote in Voetbal International.
"However, when I see Sanogo, I still have my doubts. I have still found no qualities with which you can do something.
"I think that Ajax has too little depth, the real speed is lacking, meaning that your opponent can never be surprised.
"An opponent of Ajax can therefore cope quite easily under pressure and that makes the team relatively easy to defend against."
The 22-year-old has made just 11 appearances for parent club Arsenal since signing from Auxerre and spent the second half of last season on loan to Crystal Palace but has yet to score a Premier League goal.