In an even Premier League encounter at Upton Park, West Ham endured a frustrating day as on-loan Napoli full-back Armero clumsily fouled Cameron Jerome just inside the area and Mile Jedinak confidently slotted away the resulting spot-kick after 59 minutes.
Allardyce cut a despondent figure at the end of the match and, although he feels his side should have been given a first-half penalty when Scott Dann brought Andy Carroll down, the former Bolton manager acknowledged that Armero's error ultimately cost West Ham.
He said: "We think Andy (Carroll) was fouled in the box in the first half against Scott Dann.
"As always I've had a look at the key moments after the game and of course looking at that it certainly looks like a blatant penalty to me.
"Quite why (referee) Martin (Atkinson) didn't give it I don't know, considering his position.
"Those things need to go for you but the last thing we need to do is give a silly penalty away like we did and really in the end we have paid a high price for that.
"Pablo really shouldn't have given that penalty away and in the end it has cost us."
Despite his perceived annoyance at his side's display, Allardyce pointed out that in the bigger picture football did not matter on Saturday following the death of Dylan Tombides, the 20-year-old West Ham player who lost his three-year fight with cancer on Friday.
He added: "Football doesn't mean much to me after what happened to Dylan in the last few days and when I heard the bad news about his passing.
"My thoughts have been with him and his family.
"My sympathies go to them.
"It's a sad, sad day for them and for us for a young man who put up a such a great fight to live and continue to play football."
