The Bolton manager saw an early first half thunderbolt by Kevin Davies make all the difference as Wanderers booked their place in the quarter finals for the first time in five years.
More so Allardyce was happy with the contribution of the players who came into the side such as Fernando Hierro, Khalilou Fadiga and recent signing Vincent Candela.
"I am very pleased that for the first time in my life as a manager whatever players I bring in it doesn't detract from those I leave out, Everyone is asking me what my strongest team is and I can't tell you.
"Whenever I change it the team is as strong as before, in fact sometimes we are better. We are 10 games undefeated now and conceded only four goals in that spell which is a magnificent achievement."
Allardyce also expects the Bolton public to turn out in force should the Trotters be handed a home tie in the next round.
'Every season-ticket holder had to pay for a ticket today. That is a big reason why the cup crowds are down. People want to come and watch the FA Cup but they can't afford it.
'If we get a home draw in the quarter finals you will see a difference because people will get more excited about it and will come and cheer us on.'