Cohen tweeted Wednesday about his struggling ballclub that "it's hard to understand how professional hitters can be this unproductive."
The Mets have lost seven of eight and rank 27th in the majors with 459 runs despite a lineup full of proven hitters.
Lindor has been among the bigger disappointments, hitting .228 with 11 homers and a .702 OPS in his first season after being acquired from Cleveland and signed to a 10-year, $341 million contract.
"We've been getting that message all year," Lindor told reporters before Saturday's game against the Los Angeles Dodgers. "We haven't really hit all year long. I haven't performed. I haven't done it. Bottom line, I haven't done what I'm here to do when it comes to the offensive side.
"Defense, they can't talk to me. Baserunning, they can't talk to me, either. But offensively, yeah, criticize me. Say whatever. You're right. You're all right. I'm with them. I haven't performed."
Manager Luis Rojas echoed those sentiments when asked if the team has been pressing since Cohen's tweet.
"No, not at all. These guys are working hard," Rojas said. "I made it clear the message was taken properly. The message was to keep working hard and [stay] together. We have a lot of good hitters that haven't been as good as they were in the past and they're working hard to get there.
"The message was, 'We've got to be better.' I don't think they're pressing. I don't think they're anxious because the message was from Steve. I think they took the message the best way they could."
Lindor has been on the injured list with a right oblique strain since July 17 but could return as soon as Sunday.