Allardyce is also hopeful that Liverpool will be feeling the effects of their midweek 2-1 victory over Ludogorets Razgrad in the Champions League.
"When you get possession there will be gaps and you have to try and exploit those occasions well," Allardyce said in this morning's press conference.
"We have to believe we can do that at one stage or another. We have to be defensively resilient and then when we have possession we have to exploit the gaps they may possibly leave.
"Having played with my team in Europe at Bolton I know how difficult the next Premier League game can be, so if we can seek any advantage from that then great, but Brendan does have a big squad."
West Ham currently sit two points behind Liverpool in the Premier League table after four games.