"I've not spoken to the players," he explained to reporters, "because I wouldn't know where to begin." In fact, he soon found a starting point. "Our performance was indefensible," he said, before unleashing a stream of disparaging adjectives. "What happened will not be tolerated."
It was all good, headline-making stuff but at the same time an argument against the post-match exposition that goes with being in charge. Several managers, Howard Wilkinson and Kevin Keegan among them, have questioned the wisdom of delivering a verdict while adrenalin and emotion are still running high and Strachan's rage seemed to support their point.
To the impartial observer, at least, Coventry's performance in a twice- postponed third-round tie was far from the "disgrace" of Strachan's impassioned condemnation; merely that of an inconsistent, vulnerable team at the wrong end of one over-hyped league confronted with opponents from another of sometimes underestimated quality.
The GM Vauxhall Conference houses several clubs who would hold their own in the Third or Second Divisions of the Nationwide League, and Woking, who had beaten Millwall and Cambridge in earlier rounds, appeared not only at ease in their surroundings but confident enough to eschew any thought of behaving as Cup minnows are expected to do.
Defeated only once in 14 Cup and Conference matches since October, they made defence their priority but, far from seeking to unsettle their opponents with crude tactics in attack, instead played cat and mouse, passing and probing with a degree of patience and maturity that probably took Coventry by surprise.
The Premiership side, who hit the woodwork twice in the first half and had Woking under the cosh in the minutes before Eoin Jess gave them the lead, found the greater penetration but there was little evidence of the class divide some might have been expecting.
Clive Walker's background with Chelsea and Sunderland is well known but most of Saturday's team have some League experience. Even the goalscorer Steve Thompson, the 33-year-old midfielder whose background as a former RAF physical training instructor appealed to the romantics, has more than 50 appearances (with Bristol City and Wycombe Wanderers) to his name.
Only in fitness were they at an appreciable disadvantage, the limited benefits of a two-nights-a-week training schedule exposed in the period before Eoin Jess's goal, when they were pretty much run ragged.
Where Coventry failed was that, once in front, they relaxed, apparently so sure the job was done that they allowed Woking to invade territory previously kept out of bounds. After several minutes in which the ball flew in and out of the home side's penalty area, a sequence of headers ended with Thompson, a hive of industry throughout, taking advantage of a fortunate ricochet to stab home the equaliser.
Strachan was justifiably cross at seeing a winning chance squandered but perhaps it is money that confuses his view of the broader picture. It may well have been a pounds 17m side against one that cost less than pounds 50,000; but it was also 11 men against 11 others. It will be when the sides re- engage a week tomorrow at Kingfield Stadium, where Woking, conquerors of West Bromwich Albion six years ago, have a chance to bring Coventry's Sutton United nightmare back to life.
Goals: Jess (75) 1-0; Thompson (89) 1-1.
Coventry City (3-5-2): Ogrizovic; Shaw, Borrows, Williams; Telfer, Richardson, Jess, McAllister, Salako; Huckerby, Whelan. Substitutes not used: Hall, Ducros, Filan (gk).
Woking (5-2-1-2): Batty; S Wye, Howard, Brown, Foster, Taylor; Jones, Thompson; Steele; Hunter (Hay, 80), Walker. Substitutes not used: Ellis, L Wye.
Referee: M Riley (Leeds).
Bookings: Coventry: Telfer. Woking: Howard.
Man of the match: Thompson.