"I think a lot of coaches are unhappy about it because they don't know if they are going to end the competition with the same team they started with," Platini told reporters at UEFA headquarters in Nyon, Switzerland.
"I think it's unacceptable when, in one part of the competition, a player plays for team A against team B and, in the second half, he plays for team B against team A."
"This transfer window has been created to allow for a certain amount of business in a few other situations, but I think overall it damages the competitions."
His French compatriot Wenger agreed.
While Arsenal have yet to make any new signings this month, fellow Premier League side Newcastle United have been busy with purchases including French players Massadio Haidara, Mathieu Debuchy, Yoan Gouffran and Mapou Yanga-Mbiwa.
"I think it (January transfers) should all be completely cut out or limited to two players," Wenger told a news conference.
"It's unfair for the league, some teams who have played for example Newcastle now twice already have an advantage on teams who play Newcastle now they have bought six or seven players.
"You do not face exactly the same team so I believe the number of players you could buy should be limited."
Arsenal rarely use the January transfer window, having only signed Thierry Henry on loan last season, no-one the two previous campaigns and Andrei Arshavin - whose Russian season had completed - back in 2009.
Wenger pointed out fundamental flaws in the mid-season window, which see teams both panic buy and panic sell, resulting in unusual transfer fees.
"It is a wrong transfer market. The only teams who sell players are teams who are in financial trouble who sell or players who are unhappy where they are," he added.