Overcoming the excruciating embarrassment of the 1-0 defeat to a team largely composed of part-time, semi-professionals will take much longer.
Regardless of Rodgers’ immediate and mildly alarming post-match comments to the contrary, an embarrassment is exactly what the result against Lincoln Red Imps constituted.
Not just for Celtic, but for what feels like the inexorably diminishing status of Scottish football as a whole on the European club stage.
In what is the 50th anniversary season of Celtic’s greatest achievement, when Jock Stein and his peerless home-grown side lifted the European Cup itself in Lisbon, Tuesday night was a fresh nadir.
It came just a week after Aberdeen, continental high achievers themselves under Alex Ferguson in the 1980s, came within the width of the goal frame of being eliminated from the Europa League by a team from Luxembourg.
The dismal deterioration of Scotland’s Uefa co-efficient ranking has placed the country firmly among the minnows of European football. On current evidence, it is exactly where it belongs.
Yet it was only four seasons ago that Celtic and their supporters were basking in the glory of a 2-1 win over Barcelona in the group stage of the Champions League, en route to reaching the last 16 of the tournament under Neil Lennon.
If the primary motivation in appointing Rodgers as manager was to return the club to competing regularly with that kind of elevated company, his first competitive outing at the helm provided nothing in the way of encouragement.
After two years of failure in the Champions League qualifiers under Ronny Deila, Celtic fans have placed considerable faith in Rodgers’ ability to reverse that trend. Booming season -ticket sales have been testimony to that.
Expectation will now be placed upon Celtic’s major shareholder Dermot Desmond and chief executive Peter Lawwell to provide Rodgers with significant backing in terms of player recruitment over the next few weeks if that summer feelgood factor is not to dissipate very quickly.
In order to avoid missing out once again on the £20 million bounty provided by reaching the Champions League group stage, Celtic will have to radically shake up the first team squad Rodgers has inherited. So far, the highly regarded but as yet unproven French striker Moussa Dembele has been his only signing at a cost of around £500,000.
But most of the players on duty in Gibraltar on Tuesday night were those who also contributed to some of the grim European results and performances witnessed during Deila’s tenure.
Efe Ambrose’s continuing presence as a Celtic player is a source of despair and bewilderment for their support. The Nigerian defender is an incurable recidivist when it comes to costly mistakes, his latest blunder clearing the path for Lincoln Red Imps striker Lee Casciaro to score the only goal of the game at the Victoria Stadium.
Fresh questions have also been raised over the effectiveness of Scott Brown as the driving force and captain of a side which too often lacks pace, dynamism and creativity in the midfield department.
Assuming they avoid the unthinkable next week – and that still feels like a dangerous assumption to make at the moment – far sterner tests await Celtic in the third qualifying and then play-off rounds of the Champions League with potential opponents such as Red Star Belgrade, Legia Warsaw and Dinamo Zagreb lying in wait. The Scottish champions currently seem ill-equipped to meet such a challenge.
As with any new Celtic manager, Rodgers is facing the baptism of fire provided by having these most important fixtures of their season so soon in his tenure. If Tuesday night served any positive purpose for the former Liverpool boss, it should have left him in no doubt that the group of players presently at his disposal are not fit for purpose at Champions League level.
When the best resourced and pre-eminent club in the country struggles so wretchedly to make worthwhile progress in Europe, the overall prospects for Scottish football remain bleak.
Perhaps Celtic can yet prove Tuesday night was merely an ignominious blip from which they will successfully respond under Rodgers, while Hearts, Hibs and Aberdeen might make further inroads in the Europa League.
But regardless of how the next few weeks pan out, that defeat in Gibraltar has left a stain on Scotland’s reputation which will not be easily removed.