Walker says Oliver did well after a late Liverpool penalty call for Jeremy Doku's clash with Alexis Mac Allister was waved away.
"I think the referee did really well," Walker told Sky Sports.
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"I feel once you have the Anfield crowd behind them, he could've crumbled - but that shows his experience, that shows his character.
"That's why he's regarded as probably one of the best referees in this country and the world at the minute."
On the Doku clash, Walker also said: "It's probably not for me to say if I think it's a pen. If I say it's not a pen, it's headlines. If I say it is a pen, it's headlines.
"The VAR's checked it, the ref's done it - that's all I'm going to say on that."