The champions trail rivals Liverpool by 11 points at the top of the table following a dramatic slump that has seen them lose six out of seven games in all competitions but Walker says the team will never concede defeat after winning four league titles in a row.
In an Instagram message addressed to supporters, the full-back said: "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."
City manager Pep Guardiola is on the worst winless run of his managerial career but has vowed to lead the club through their difficult spell.
The coach said: "When I was in trouble my mum and dad never gave me away. Always they were there.
"Now I have the feeling in the club, I want to be with these players. We didn’t think we could lose one game, two games. Losing six or seven is ‘wow’, it is a lot, but it is what it is, accept it."