City still face a battle if owner Sheikh Mansour's stated aim is to be achieved.
But with so much class at their disposal, and new manager Roberto Mancini already making his side into a more durable defensive unit, Allardyce feels City fans have good reason to be optimistic.
"There is no reason to think they cannot be in the top four," said the Blackburn boss.
"When you look at the other sides who usually finish in the top four, it might not be a bad time to do it.
"Some of the big clubs are not living up to their normal standards.
"Liverpool and Manchester United are not quite as good as they have been, so an opportunity could be there for Manchester City.
"They have quite a few injuries themselves and they are still fourth.
"They have also won four matches on the trot under Roberto Mancini so confidence is bound to grow as well."
A very unhappy Allardyce was left to reflect on a ninth game without a win and a punishing defeat, which comes just three days before Thursday's Carling Cup semi-final with Aston Villa at Ewood Park.
"I could not believe what we were doing in the first half," groaned Allardyce.
"It was a bad night for us and the players did not live up to their regular performances."
Source: Team Talk
Source: Team Talk