"We have to capitalise on the drain of confidence they must be feeling," said Allardyce.
"If we keep the game nil-nil and tight, then the longer it goes on, the more anxiety will creep into their players and we have to make the most of it.
"Portsmouth's problem is that they have not achieved what they normally achieve on their own soil.
"This season they have been very passionate and very committed but they have lost too many games at home and that's why they are in the position they are in.
"When you are in that position, things seem to go against you and we have to capitalise on that."
"We'll have to compete first and try to capitalise on what mistakes they might make or produce some quality," he said.
"Portsmouth won't give us any room to play the sort of football we've been playing recently so we'll have to battle it out first and earn the right to play.
"The first thing that is going to be asked of my players is a passionate, battling, determined performance against a Portsmouth side which will have its sleeves rolled up and full of blood and thunder.
"We'll have to match that.
"It might help us that they might be slightly more fatigued than us because they played their cup game on Sunday while we played on Saturday and we've got to use that to our advantage as well.
"But we have a team that is full of confidence and playing to the best of its ability and if we do that we will get a result."
Meanwhile, Fabrice Fernandes has reportedly joined Israeli side Betar Jerusalem after Bolton cancelled his contract on Tuesday.