Unai Emery's side missed out on the chance to go third in the Premier League as Lys Mousset sent Bramall Lane into raptures with the only goal before half-time.
The result prompted familiar discussion of Arsenal's vulnerability to such setbacks, with former France and Manchester United defender Evra suggesting it is a weakness long entrenched at the club.
"I used to call them 'my babies' 10 years ago, and they are still, when I look at them, 'my babies'. That’s the truth,” he said while working as a pundit for Sky Sports.
Xhaka, who made way for Alexandre Lacazette as Arsenal chased an equaliser in vain, was uncompromising in his response.
"We have to stop speaking about mental [issues] or bulls*** like this," he told reporters.
"For me it's the same if you play home or away. You have to win. You have to show big character. You have to show good games and not to find always the same excuse.
"A lot of people speak too much. I hear that the first time he [Evra] speaks something against us. I have a lot of respect about him, because he was a great player. But you have to be careful what you say in those situations as well.
"It’s not only him it's a lot of people. They speak a lot of bulls*** about us. It's always the same.
"For me it’s strange because they [pundits] were in the same situation as us, they were players as well.
"Maybe sometimes it was good, sometimes it was not so good. But if you speak every weekend, every game, bulls*** like this they speak, they don't get respect about what they say.
"I tell you the honest [truth]. I'm not interested in what people say and speak. We have to speak in our group to improve things and work hard."
Xhaka rued Arsenal being undone by a set piece and insisted there were positives in Arsenal's display.
"Of course it's frustrating because it's so easy. It's too easy if you lose the game because of a corner or free-kick," the Switzerland midfielder said.
"We have to improve things. We had good things as well. We were compact in defence. They didn't have a lot of chances. But if you want to be in the top four you have to beat Sheffield.
"I think we did a lot of good things. I think Sheffield had one chance, it was the goal. That's it."
Arsenal hosts Vitoria Guimaraes in the Europa League on Friday (AEDT) before preparing for a weekend derby at home to Crystal Palace in the Premier League.