Instead of bringing world-class invention and danger to a Scotland team he is now employed to organise a side without those qualities. This, his first match as manager of the national team, delivered a reasonable performance and a win courtesy of Charlie Mulgrew's intelligently-made goal just before half-time.
Just over 16,000 came out to watch it on a cold February night in Aberdeen. Strachan can take encouragement from two things: they stayed to the end and applauded at the final whistle, which is more than could be said of a few other Scotland games recently.
No-one will have started booking flights to Rio on the back of it, but there was nothing to puncture the sense of momentum created by Strachan's appointment, and which will now extend to his first World Cup qualifier at home to Wales on March 22.
All that was truly new about last night was the identity of the manager and the mood towards the team: one of renewal and hope. Scotland had had enough of Craig Levein and has come to will Strachan to succeed. But there was no prospect of him trying to endear himself further with a showy cull of the squad he inherited. Five of the starting team last night were also on at kick-off in Levein's last game against Belgium and that would have been seven if Darren Fletcher and Gary Caldwell had been available.
By and large it was the same collection of players Levein used – albeit with Chris Burke as a refreshing introduction in his first Scotland appearance for nearly seven years – and for the first half it was the same system, too. Scotland played 4-2-3-1, the same shape Levein deployed in the World Cup qualifiers against Macedonia and Belgium.
The formation and more than half of the personnel changed in the second half. In truth the performance was indistinguishable from some of the low-key friendly victories in Levein's time. Any win is welcome, though, and the display was not without positives which will nourish Strachan until the qualifiers against Wales and Serbia.
Burke vindicated the decision to recall him from international exile, giving a zestful first-half display on the right wing. Alan Hutton, Andy Webster, Christophe Berra and Charlie Mulgrew – no-one's idea of a reassuring back four – were lined up behind two deep-lying midfielders, Scott Brown and Charlie Adam. Burke had Shaun Maloney buzzing in the centre and Steven Naismith on the left, all three working to support Steven Fletcher. The balance was good but Burke and Maloney's displays eclipsed all others except Allan McGregor.
Before kick-off Strachan had lamented the wind and rain as factors which might preclude his men playing attractive football. The Pittodrie pitch, looking heavy, was to their disadvantage too. If a lack of invention and penetration was inevitable given the team's limitations it was at least tolerable for supporters given the generally crisp and hard-working nature of the overall performance.
One attack allowed Burke to lift a cross to Fletcher, whose header plopped on to the roof of the net. The striker needs to start adding goals to expectation in Scotland colours and he looked sharp around the ball although not especially dangerous. Maloney offered more, worming his way into a pocket of space but his low shot which was saved by Sergei Pareiko.
Strachan was entitled to purr over the opening goal. It has the unmistakable look of a move, and an execution, performed by players who know each other's talents. Adam stood over a free-kick on the left as Scotland players and their markers populated the edge of the six-yard box in apparent expectation of a floated delivery. Instead something else was planned; Mulgrew peeled off into space near the penalty spot and Adam knew to play it low and square to him, allowing the Celtic man to meet the cross with a crisp finish into the corner.
Estonia, who reached the Euro 2012 play-offs, were by no means outclassed. It was just as well Taijo Teniste had his hands full coping with Burke because, when he pushed forward, he showed vicious shooting ability with a couple of long-range efforts, one of which needed a fine save. McGregor was also required to block a shot from Tarmo Kink, a player Strachan signed for Middlesbrough, when he was put through on goal.
Strachan looked at five more of his men in the second half, with the introduction of Jordan Rhodes meaning the shape moved to 4-4-2. Although the Blackburn Rovers striker could not add to his three previous goals he caused a ripple of excitement by taking a fine Christophe Berra pass and peeling off a defender to try a dangerous shot. Robert Snodgrass, James McArthur, James Morrison and Kris Commons redrew the midfield and Kenny Miller replaced Fletcher in attack.
Only the back four remained intact throughout and a clean sheet did them no harm. On his opening night, no damage was done to Strachan either.