And the Scotsman has taken a subtle jab at Unai Emery’s inconsistent side in the aftermath of the Bramall Lane clash, admitting that the Blades now face tougher tests.
Lys Mousset scored the only goal of the game, turning home unmarked from three yards.
Arsenal never really looked like grabbing an equaliser, failing to truly test goalkeeper Dean Henderson as Chris Wilder’s men stood firm.
Now Fleck, 28, has offered his own damning indictment of Emery’s side.
“We’ve done well so far but we know there are tougher games to come.
“We move on to a difficult game against West Ham . For us it’s just the same every week.
“There will still be difficult moments this season but against Arsenal we got our rewards.”
Fleck added: “It’s obviously great for the fans that we got a result.
“The problem with the last few games at home is we have played well and got nothing from the games so it was important that we got a big victory and we have done that.
“I’m not too sure how people will react to it. For us it’s just the same every week, we always try and work as hard as we can and get our rewards at the end of the game and on this occasion, we’ve done that.”
Victory ended a run of three successive home defeats and moved United up to ninth in the table.
Wilder’s side face West Ham this weekend at the London Stadium, with talkSPORT presenter Jason Cundy claiming he could be the right choice to replace Unai Emery at Arsenal, if the Gunners were to dispense with the Spaniard.
“Look at the way Wilder set his team up on Monday,” he declared on Monday. “Arsenal need a manager who’s astute defensively, but still carries a threat going forward.
“Chris Wilder is working on a completely different budget but he outclassed Emery. Could they do any worse than Chris Wilder?
“There’s a lot of things to like about him. Where he came from, he’s humble and speaks the truth. Look at his comments about his goalkeeper [Dean Henderson] recently.
“Arsenal need someone [like him]. Could he get a tune out of Mesut Ozil? I don’t know, but that’s what they need.
“Can you imagine Chris Wilder managing Arsenal? You can’t, because they wouldn’t go for someone like that. He’s seen as unfashionable. But could he have turned Arsenal into a different animal since Arsene Wenger left?”