The right-back is aware of how much the club is under scrutiny after going seven games without a win.
City are 11 points behind in the title race and may even struggle to finish in the top four on this form.
He posted on Instagram, a day after a 2-0 away loss to Liverpool: "We know our recent performances haven’t been up to the standard we expect, and we’re aware it’s been tough.
"But we’ve been through these challenges before, together, and we’ll come through this one as well.
"It’s important that we all stay together as one club, as Manchester City, through this tough spell. Your support, whether in the good times or the difficult moments, means everything to us.
"We’ve won titles in the final games of the season, and we’ve made history with a record-breaking 100-point campaign, right down to the last kick.
"We’ve shown time and time again that we can rise to the challenge, and we will do so again.
"I promise you, we’ll fight until the very end."
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