The Hammers have shipped 11 goals in their last two matches, losing 5-0 to Nottingham Forest in the FA Cup and 6-0 to Manchester City in the Capital One Cup semi-final first leg.
But Premier League survival takes precedence and, despite reassuring noises from the West Ham board, Allardyce knows he must arrest the alarming run of form swiftly.
He said: "My most important two games now are Cardiff City and Newcastle, before we get to the second leg. That is the biggest and major concern for me, getting up and getting the lads ready for that."
He will find a Cardiff side buoyed by their first victory at Newcastle last weekend for 51 years, a triumph which was inspired by two second-half substitutions by new manager Ole Gunnar Solskjaer, who has made an approach to sign Hannover striker Mame Biram Diouf.
Michael Laudrup's Swansea face a chastened Manchester United at Old Trafford six days after dumping them out of the FA Cup.
Another defeat for United would mean four losses in a row for the first time since 1961. Laudrup, however, will be without the injured Michel Vorm, Michu, Dwight Tiendalli, Jonathan de Guzman, Pablo Hernandez and Roland Lamah.
Laudrup said: "It will be more difficult than last week. I expect United to come out and really go at us. They have to win this game so we have to be ready."
Crystal Palace boss Tony Pulis goes to Tottenham determined to claw his way out of relegation trouble by strengthening his squad astutely.
"I don't want to be bringing in players who just want to jog through six months," Pulis said.
"We need people who are going to roll their sleeves up, work hard and make a difference and add to what we've got already. We need to get deals done if we're going to push on."
Everton manager Roberto Martinez wants his side, currently in fifth position, to kick on in the quest for a top-four place with the emphasis on keeping the squad intact.
They play Norwich this weekend and Martinez said: "The youngsters have developed extremely well to have important roles in the side. In January we don't want to lose any of the top performers that we had in the first part of the season."
Norwich, meanwhile, insist midfielder Wes Hoolahan remains an important member of their squad despite being linked with Aston Villa.
Hull take on Chelsea with Steve Bruce's side hoping to add to a fine record at home this season which has seen them gain five wins and three draws from 10 matches.
They lie in 10th place in the table but defender Paul McShane will be missing for up to a month after injuring his ankle in the FA Cup victory over Middlesbrough.
Sunderland, who travel to Fulham, are hopeful they can seal a deal with Estudiantes defender Santiago Vergini this weekend.
Black Cats boss Gus Poyet said: "He's big, so he's good for England, he reads the game well and he is a good defender. Let's hope he can adapt quickly if we get him."
Southampton host West Brom with manager Mauricio Pochettino insisting the much-publicised complaint about referee Mark Clattenburg, concerning alleged remarks made to England midfielder Adam Lallana, has been consigned to history.
Meanwhile, Manchester City will top the Premier League on Sunday if they beat Newcastle at St James' Park while Liverpool, whose manager Brendan Rodgers has been fined £8,000 and given a warning by the Football Association for his criticism of referee Lee Mason, travel to Stoke.
Monday's match sees current league leaders Arsenal travel to Aston Villa.