And Coleman is adamant his side can go on to make the quarter-finals of the competition despite a recent resurgence from Rovers which has seen them lose just two of their last 12 games.
The Sky Blues, on a similar run of just two defeats in 13, lie eight points off the play-off places in the Coca-Cola Championship and Coleman believes Saturday's 1-0 win over Birmingham can give his players the confidence needed to see off Allardyce's side.
Coleman said: "It's the FA Cup and anything can happen. This result, in terms of confidence, should help us.
"We could have lost 3-0 on Saturday and gone on to win tomorrow night because the FA Cup throws up incredible results."
A glamour tie with Chelsea awaits the winner and Coleman added: "Blackburn will still be the fancied team, being the Premier League side, albeit they are in our back yard.
"But why can't we beat Blackburn, which is not impossible, and then Chelsea in the quarter-final?
"That's what we have got to look at and if we get it right on the night, we have got a good chance."
A last minute Christopher Samba strike earned Blackburn a replay after Aron Gunnarsson and Michael Doyle had put the Sky Blues ahead following Roque Santa Cruz's second minute goal.
And former Real Sociedad boss Coleman has urged the fans to turn out in force and create a cauldron of noise at the Ricoh.
He said: "I thought our supporters were brilliant on Saturday, absolutely fantastic.
"They were terrific at Ewood Park and then Burnley the other night, at the Ricoh against Wolves and again against Birmingham on Saturday.
"We keep on drumming that home to the players that if they keep winning, they will be there for us.
"They get excited when they see full-blooded performances, goals and points because that means you are going in the right direction, and then they turn up and are vocal."