Cano was part of an easy double play after he didn't run out of the box in the fourth inning of Sunday's loss to the Miami Marlins.
The incident followed a similar one on Friday when Cano failed to run out a ground ball during a different double play. He later said he was fooled by a scoreboard that read two outs.
"Things are piling up on Robbie right now," Mets skipper Mickey Callaway said when asked about Cano's two separate failures to run, according to SNY's Steve Gelbs. "He hit into a double play. The ball lands foul and spins into fair territory. He hit it. He looked down and saw it hit foul and by the time he looked back up the ball had spun into fair territory and the play was over.
"He realizes he has to run. It's not like he's doing that on purpose. Anybody in their right mind knows that nobody would do that. It's just piling up on him and it's tough. Stuff happens like that when things are going bad."
Asked if Cano should have been pulled from the game, Callaway continued to support his second baseman. "I'm not defending not running down the line, but you've got to have a little common sense when something that doesn't happen very often happens.
"I didn't feel that that was enough to warrant taking him out of the game at that point."
Cano appeared aggravated with reporters when asked if his misplays made for a bad look.
"I don't want to say it's a bad look," he responded, according to Andy Slater of 640 The Hurricane. "Like I said, I thought it was foul like anybody else. I mean, I got hit twice in the hand and they called it a strike and none of you guys asked me anything about that."
The Mets have now lost five straight following a three-game series sweep by the last-place Marlins.
New York's losing streak has led to speculation that Callaway could soon be relieved of his duties as manager.