The fate of Burns as Celtic manager will be determined at the end of the season and while even a cup might not be enough to keep him in his job he knows defeat at the hands of the First Division outfit would hasten his departure.
Saturday's game at Ibrox betrayed the main reason Burns' position is under threat. His side, which has been assembled at a cost of pounds 16m, has consistently failed on the big occasion. A cup win at the end of his first season in charge proved a false dawn in terms of trophies and the fact that Rangers are close to equalling Celtic's nine-in-a-row league record serves merely to underline Celtic's current lack of success.
Celtic have lost all four Premier Division games against Rangers this season for the first time since the top league was formed more than 20 years ago, and while Rangers were beaten in the Cup quarter-final, Celtic have failed to win any of their five subsequent matches. Defeat by Falkirk would be the final straw.
Burns has asked to be judged on the job he has done: to do so is to recognise that the playing side has improved dramatically with Celtic again competing for the league title after several disappointing years, but if a manager is to be judged by results, Burns has failed to deliver.
His job has been hindered, however, by internal politics that threaten to negate the progress the club has made both on and off the field. The manager has had his hands tied in contract negotiations which have been conducted by Fergus McCann, the chief executive, whose abrasive style has led to Pierre van Hooijdonk leaving for Nottingham Forest as well as unrest among several other players.
Saturday's game was drawn after Celtic took the lead through Tommy Johnson, their recent signing from Aston Villa, and despite dominating for long periods they were unable to convert that domination into more goals.
The crushing blow was a headed equaliser eight minutes from time by Kevin James, a central defender who was pushed forward after Alan Stubbs was taken off with concussion.
A parallel with the League Cup final defeat at the hands of a Raith Rovers side inspired by Jimmy Nicholl is an easy one to make. However, that occasion marked a substantially low point for Burns and the club.
"We are disappointed to have made so many chances and not won, but we'll come back a week on Wednesday and get the job done," said Burns.
His counterpart, Alex Totten, acknowledged the significance of the loss of Stubbs, saying, "Celtic lost their tallest player and that was why I sent James into attack. The greatest sight for a manager is 11 players giving everything they have got and that's what I had today."
Burns will be hoping that his side display a similar kind of unity in the replay.
Goals: Johnson (65) 1-0; James (82) 1-1.
Celtic (4-4-2): Kerr; Annoni, Stubbs (McNamara, 50), Boyd, McKinlay; Thom, Hannah, O'Donnell, Di Canio; Johnson, Cadete.
Falkirk (5-3-2): Nelson; McGowan, Gray, Oliver, James, Seaton; MacKenzie (Craig, 74), Hagen, McGrillen; McAllister, Crabbe (Fellner, 74).
Referee: W Young (Clarkston).
Bookings: Celtic: Stubbs, McKinlay. Falkirk: Gray, Nelson, McAllister.
Man of the match: James (Falkirk). Attendance: 45,261.