The Englishman spoke about their tight title triumph over the Gunners, who finished runners up.
City won the league for the fourth straight time, with Arsenal coming second for two successive seasons.
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The manager (Pep Guardiola) said after the interview on Sky the other day when he said we've got the message and we hear it loud and clear," Walker said.
I think for him to say that, he knows Arsenal are right on our heels now so either we need to up our game a little bit more or Arsenal need to fall off a little bit.
The gap is getting closer each year, it's getting closer. We need to probably extend that gap to give ourselves a little bit of breathing space."