A week after beating the Gunners 5-1 in the Premier League, Liverpool crashed to a 2-1 defeat at the Emirates Stadium to end their hopes of FA Cup glory this season.
Webb stands accused of not awarding a penalty when Alex Oxlade-Chamberlain looked to have fouled Luis Suarez in the area.
In a column for the Liverpool Echo, Aldridge said:
How many of these wrong decisions does Webb have to make before action is taken?
For a start, he should never referee a Liverpool game ever again. The Reds can go back in the archives and use a long list of games to help state their case.
When he refs us, we do not get the big, big decisions and with Liverpool chasing at least the top four, we must hope he does not officiate our games between now and the end of the season.
Howard Webb costs us. Plain and simple.
Aldridge is not the only one to criticise Webb for his performance on Sunday.
Speaking to the Alan Brazil Sports Breakfast show (via Alex Varney of talkSPORT), former referee Mark Halsey claimed that Webb has too much on his plate and could need a rest:
Howard has made an error of judgement. He has not had the best of seasons. He has not been the Howard Webb we all know.
Perhaps he may need a little rest because he is perhaps doing too much.
Meanwhile, in the Mail Online, another former referee, Graham Poll, labelled Webb weak and said that the error will be a lingering memory now:
Webb, of course, with his experience and pedigree, should do better and be above such weakness — Liverpool are now out of the FA Cup because he wasn’t.
Webb contributed well to an absorbing cup tie between Arsenal and Liverpool - but all his good work will be forgotten because of one error.
Even The Daily Telegraph's chief football correspondent, Henry Winter, admitted it was a bad day at the office for Webb:
Despite these criticisms, it has to be remembered that whether he made the right call or not, Webb only had a split second to make the decision.
Having refereed the 2010 World Cup final between Spain and the Netherlands, Webb is of a standard that is usually suitable for top matches.
But after making a wrong call, it has to be accepted that referees can have bad days, too—in the same way that players can.
It has cost Liverpool on this occasion, but that is part of football. It is not a game where decisions are able to be made in a cut-and-dried scenario, and if it were, it would be a much poorer sport for it.
Aldridge's assertion that Liverpool should be exempt from Webb's refereeing is ambitious at best and will not happen. He is talking emotionally and not with common sense.
If that were to happen, it would give managers more power over officials and more ability to influence decisions than ever before, making a referee's job even harder than it already is.