Allardyce's side go to the Emirates on the back of nine days' rest, while Arsenal have had just three days to recover from 120 minutes at Wembley on Saturday.
Arsene Wenger is already hampered by the absence of several key players and must now assess several more in the wake of that FA Cup semi-final against Wigan.
Those problems are not lost on Allardyce, who will order West Ham to keep pace with Arsenal early in the game and wait for fatigue to kick in.
He said: "I think we all suffer in spells of difficulty when players can't recover in time and you factor in injuries that you have. We all know that weakens your team.
"Certainly with Arsenal's game load and some of the injuries they have, then yes they will be weaker than they possibly could be.
"But they keep a Champions League place for all those years. They keep a squad of 25 international players and they're playing at the Emirates, so whatever difficulties they have it's still a hugely tough fixture for ourselves.
"Whatever team Arsene puts out, we still have to play at our best to get a result, particularly on their own patch.
"If we can seek an advantage by those problems that they have then it gives us a better chance of getting a result. It won't be any easier than it ever has been to get a result at the Emirates because the players that are actually playing won't fatigue until later in the game.
"It won't happen in the beginning of the game and we'll have to be on song from the start and fully focused on the job we have to do to try and get something."
West Ham go into the game on 37 points - one short of the survival target set by Allardyce last month and seven clear of third-bottom Fulham, who won on Saturday.
He said: "From our point of view the success of the teams below us at the weekend means we still need to take more points."
Watch Arsenal take on West Ham live from 7.45pm on Sky Sports 1 on Tuesday