Gunners supporters were visibly enraged when the manager withdrew the teenager, who was having an impressive game, replacing him with the increasingly frustrating Andrey Arshavin for the final 16 minutes of the game at the Emirates Stadium.
Robin van Persie also looked bemused by the decision on the pitch, standing with hands on hips and appearing to say "no" when the change was being made.
The fans' reactions were worse following United's winner, scored when Antonio Valencia took the ball past Arshavin before setting up Danny Welbeck and Szczesny was cautious about condemning the supporters for their disappointment, saying that they are entitled to their opinions.
"I don't want to say something that I shouldn't be saying," Szczesny told the Press Association. "They're entitled to their opinion and they show it in the way they do. That's fine with me. There's a lot of pressure. Obviously fans expect us to do better than what we've been doing. All we can do is work hard, which we have been doing, and I'm positive the results will come sooner rather than later."
Wenger has said that it would be a "disaster" for Arsenal if it failed to qualify for the Champions League, and Szczesny agreed with his manager.
"This club should be in the Champions League year in, year out," he continued. "So I understand the manager's point, obviously. I'm confident we will pick ourselves up, we'll win games and we'll get our position in the Champions League. So I'm not worried. I'm disappointed, obviously, but I'm still confident we can do it."
Szczesny also defended the players to have joined the team this year, but admitted the return of players such as Bacary Sagna and Kieran Gibbs would be a huge boost.
"All the players that came in, they did well for us," he said. "They're doing their job as well as they can and that's all you can ask for. [Gibbs and Sagna] are important players for us and if you can have them back in the team as soon as possible, it will give us a lot of confidence and hopefully it will help us to get the results that this club deserves."
The Pole was also quick to praise Oxlade-Chamberlain and captain Van Persie for their performances in the game.
"[Alex Oxlade-Chamberlain] did what you expect Alex to do. He runs past people, he puts good crosses in, I think he actually had an assist for the goal, didn't he? He was very positive and I'm sure that it's a moment he will remember," the goalkeeper enthused.
"Robin is a great player. I've said it a lot of times before, I think he's the best player in the Premier League at the moment," he added. "Listen, we are disappointed. But we're still confident we have the quality. And it's not only Robin van Persie. I think the whole team is good enough to go on and finish in the top four. Having a leader like this - because he's a great skipper - helps the team. It makes us confident that we can score in every single game."