"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."
Wenger did not rule out bringing in new players in this window but reckoned it was not necessary for the club.
"If someone else can strengthen our squad, we will do it of course, but we have the resources inside to do well," he said.
"We have two players in every position, that should be enough, plus the young players in behind.
"But if we find the top-class players in any position, we never refuse to strengthen our squad."
He pointed out fundamental flaws in the mid-season transfer window.
"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 said.
Arsenal, who are sixth in the Premier League, will turn their attention to the FA Cup this weekend when they head to Championship Brighton and Hove Albion in the fourth round.
They will be without injured captain Thomas Vermaelen who sustained a minor ankle injury in Wednesday's 5-1 thumping of West Ham United in the league but will welcome back midfielders Abou Diaby and Tomas Rosicky.
"[Vermaelen's injury] is short term. It got a bit worse yesterday so we will not gamble on him," Wenger said.
