It was a difficult afternoon for the 34-year-old, who ended up on the losing side and was involved in the build-up to Arsenal’s second goal when goalscorer Gabriel Magalhaes got away from him.
Walker was caught on camera blaming himself for the goal after switching with Jeremy Doku to mark the Brazilian centre-back.
He was also frustrated with Oliver ahead of Arsenal’s first goal, where Riccardo Calafiori scored a stunning left-footed strike from just under 25 yards.
Sky cameras missed the fact that Arsenal had taken a quick free kick in the build-up, which caught the City defence off guard, leaving them out of position.
Although no infringement was found, City players were still visibly unhappy.
As reported by BBC Sport’s Simon Stone, Walker confronted Oliver in the tunnel at half-time and “made his point” regarding the incident.
Earlier, City players had surrounded the referee immediately after Calafiori’s goal.
Speaking to BBC Radio 5 Live post-match, Walker explained his exchange with the referee: “I didn’t go over to the referee. Me and Bukayo Saka didn’t approach him. He called us over.
“So, if the referee calls me over, he should then wait and allow me to get back into position before the ball goes over my head.
“Me and Mike have a good relationship, and I think he does a great job. This isn’t me being critical of him. I know his job is tough.
“If I went over of my own accord, then it’s fair game [to restart].
“But for him to call both captains over and then not let me get back in position… if I were a goalkeeper, would he let me return to my net? Of course. I’m a defender, I’m the first line of defence. He should allow me to get set, then blow the whistle.”