The Baggies took the lead in the 12th minute at The Hawthorns when Craig Dawson was allowed to roam free in the box and head home from a corner.
Arsenal hit back moments later when Alexis Sanchez fired home from close range to level the score.
But West Brom were ahead once again in the 55th minute when Hal Robson-Kanu bundles home from close range and Dawson scored again from a corner in the 76th minute.
Redknapp was particularly unimpressed by Ramsey’s showing in the first half as he failed to pick up on Dawson’s run for the opener.
Speaking to Sky Sports at half-time, former midfielder Redknapp said: “No one is in there saying who is marking Craig Dawson. It’s too simple. It’s a disgusting goal to concede.
“Aaron Ramsey – who should be a leader – he has to pick him up, he has to get tight and block the run. Instead, it’s just so easy. No leaders.”
Arsenal are through to the FA Cup semi-finals and will play Manchester City in the last four but have a fight on their hands to qualify for next season’s Champions League.
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