With injuries decimating his squad, Mancini felt compelled to name six youngsters in his starting line-up, three of whom were making their first-team debuts for the Eastlands outfit.
Although Mancini did eventually introduce James Milner and David Silva in a desperate search for an equaliser, it was not enough to stave off an embarrassing reverse that blocked off one route to a trophy at a disappointingly early stage.
Now City must bounce back in Saturday's eagerly-awaited Premier League crunch with leaders Chelsea, knowing the heat is starting to be applied to a squad that has been put together at a cost of over £200million.
"When you are at a club like Manchester City and you spend £200million on players you expect silverware," said Cox.
"Mancini has to deal with that and a lot of questions are going to be asked.
"This was a good opportunity for them. Their manager has stuck out a team he thought would win the game and they didn't, so he could be under a bit of pressure."
When the world was marvelling at the number of big-name players arriving at Eastlands this summer, it could hardly be anticipated Mancini would be complaining at a lack of bodies quite so soon.
But Jerome Boateng is yet to make an appearance, Aleksander Kolarov and Mario Balotelli have managed just one each, while Emmanuel Adebayor, Wayne Bridge and Joleon Lescott have missed the majority of games so far this term.
Now Micah Richards and Shaun Wright-Phillips have joined the list of walking wounded.
Richards has not been able to train due to a hamstring injury he suffered at Wigan on Sunday, while Wright-Phillips reported a knee problem yesterday morning that ruled him out of contention.
Mancini is expecting to have only 13 outfield players available if Richards does not make it, which would force him to use either Gareth Barry - who did the job earlier in his career - or James Milner - who has done it on an emergency basis for both Aston Villa and England - as a makeshift left-back against the only side still to boast a 100% record.
At least City will not have to cope with the added problem of facing opponents more keen than usual to beat them.
"Last night was a big showcase for us," said Cox.
"Shay Given, Patrick Vieira and Roque Santa Cruz were all in their team, and they did not go to Manchester City for peanuts.
"You are talking about £20-£30million players. They came to our place with big reputations and we had to stand up and be counted, which is exactly what we did."
West Brom, who today allowed striker Chris Wood to join Barnsley on a three-month loan, have a big match of their own on Saturday, when they tackle Arsenal.
Roberto di Matteo is at least picking from strength, unlike Mancini, who needs to find out who is fit before he can formulate his plans.
Although a single reverse with a side packed with youngsters at a ground less than half-full does not appear a reason for recrimination, the knowledge Chelsea, Tottenham and Liverpool are out already, means it was undoubtedly the easiest opportunity City would have to end a trophy drought dating back to 1976.
Should they fail to end Chelsea's winning streak, Mancini will find the spotlight shining upon him more intensely than at any other stage of his short City reign.
"If we had been playing Chelsea on Sunday instead of Saturday I would probably have played with two or three young guys and seven senior players," he reflected.
"In the end, this defeat could be a blessing in disguise but at the moment, all our thoughts are towards Chelsea."