Wenger, who has been in charge of Arsenal since 1996, was on the receiving end of booing from sections of home fans on Sunday after substituting the impressive Chamberlain for the out-of-form Andrei Arshavin in the second half.
Gunners captain Robin van Persie also appeared angry at the decision, which was followed by a winning goal for United, although the Dutchman has since clarified his stance, expressing his backing for the French coach.
And Szczesny has echoed Van Persie's comments, stating: "He's done a magnificent job over the 15 years and he's still doing it now. So I don't think his position at this club should ever be questioned."
Chamberlain, who was making his first Premier League start for Arsenal against United and assisted Van Persie's equaliser, also voiced his support for the boss.
The teenager said: "He's Arsene Wenger, a top-quality manager for a number of years for Arsenal. He's done a lot for this club so whatever he does and whatever decision he makes towards me and the team, I'll have to respect and I do respect that.
"The fans pay money to come and watch us so they have the right to have their own opinions and show their frustration. But all we can guarantee and I can guarantee is the boys are completely focused on the task at hand.
"We have meetings in the week and we talk about what we need to improve on. Everyone is trying to push in the same direction and maybe it's not going for us how we may like at the moment.
"Recently, we've had some very good performances but come up against some very good teams. We've just fallen short at the last hurdle. All we can guarantee is we're working very hard in training and in games and we'll do all we can try put it right."