It is rare to praise the tactical decisions of a losing manager, but Roberto Mancini's strategy after Vincent Kompany's dismissal yesterday afternoon was extremely effective – despite a nervous few moments before half-time, and despite the overall defeat.

One of the greatest challenges any manager can face is going down to 10 men midway through a match. In his early days at Arsenal, Arsène Wenger said that he practised playing with 10 men in training, so his players were familiar with the situation and understood how their roles changed. His side picked up far too many red cards at that point – but when they did, they were always well prepared.

Much of tactics, at least in terms of pure positioning, revolves around outnumbering the opponent in a certain zone and then making the most of that advantage. Doing this when outnumbered overall is clearly extremely difficult. Mancini's problems were exacerbated by the fact Manchester City were already trailing – sitting back and hanging on was not a possibility here.

Of course, there is no such thing as an ideal formation when playing with 10 men, the same way there isn't when playing with 11. That said, in this situation it did seem logical for Mancini to shift to three at the back – that system is most effective when playing against two strikers, and that's the challenge United offered, with Wayne Rooney dropping off Danny Welbeck upfront.

But Mancini's change was unusual, because he shifted away from his usual defensive base of a back four. He waited until half-time to do so, however, meaning the decision was wise both in nature and timing. It would have been extremely dangerous to switch to a back three immediately after the red card in the 12th minute, without briefing the players on their new responsibilities in a system they had never played in before.

Mancini's one error, however, was that he didn't make an immediate substitution to stabilise his defence. He initially reacted to the red card by moving Micah Richards to centre-back, while James Milner dropped to right-back. The defence did not look solid and conceded two goals, while Milner's mobility was absent from midfield. Considering Mancini was to bring on Stefan Savic at half-time anyway, he should have made that switch earlier, while keeping the four-man back line until the break.

With David Silva and Adam Johnson sacrificed, Savic was joined for the second half by Pablo Zabaleta in a 3-4-1-1 shape. Savic played alongside Richards and Joleon Lescott at the back, Zabaleta and Aleksandar Kolarov were the wing-backs. Milner was back in the centre alongside Nigel de Jong, while Samir Nasri played just behind Sergio Agüero.

The back three was the building block for the energy City showed after the break. With a spare man in that zone, it gave the two outside centre-backs the freedom to move forward and bring the ball out of defence. Richards did that excellently, storming forward to win the free-kick that resulted in Kolarov's goal. Mancini then made another subtle switch to increase the potential of attacks like this – Lescott had started the second half in the middle of the three centre-backs, but he was swapped with Savic and moved to the left, presumably as Lescott is the player more accustomed to having the ball at his feet in the left-back zone.

With the back three in place, the wing-backs also had freedom to move forward into attack. Kolarov and Zabaleta stretched the play and made up for City's numerical disadvantage with sheer energy and stamina. Even if City lost the ball and either was bypassed, Richards or Lescott could move out of defence to cover, depending on which side the ball was on. The other would tuck in and become more central, and City still had two defenders marking two strikers.

With a man fewer, you re always going to be weak in one zone, and the one thing City could not do was close down high up in midfield. Nasri tired quickly, and Sir Alex Ferguson's use of Scholes was designed to keep possession and frustrate City. According to Opta, Scholes completed more passes in his half-hour on the pitch than any City player did in the duration of the game, though his one misplaced pass led to City's second goal.

The strength of City's system was underlined by the substitutions Mancini made. It must be rare for a manager to make his side a more dangerous attacking threat by removing his three creative midfielders – Silva, Johnson and Nasri - and replacing them with such functional players. Savic is a pure centre-back, Zabaleta is a defensive utility man, Owen Hargreaves is a versatile, sensible holding midfielder. Milner, another who is favoured for his ability to carry out the manager's instructions, also remained on the pitch.

City did not get the equaliser, but "won" the second half 2-0 despite being a man down, and were the more dangerous side in the final 10 minutes – in contrast to United's response to going down to 10 men in the 6-1 Premier League defeat in October. It was a tremendous piece of improvisation from Mancini, probably inspired by something he had learnt at a Coverciano coaching course. Frequently cast as a "typically Italian" manager with too much of a focus upon systems, in this game Mancini showed that does not always mean negative football – even with a man sent off.

Redknapp's forward thinking

Harry Redknapp is not quite the tactical Neanderthal often claimed, as Jonathan Wilson has written about previously, but in recent weeks he has certainly gone against conventional wisdom. After telling Gareth Bale and Rafael van der Vaart they could "play where they wanted" in the excellent win over Norwich City in late December, this weekend he fielded a midfield lacking anything close to a ball-winner, with Giovani dos Santos, Niko Kranjcar, Steven Pienaar and Aaron Lennon strung across the middle. It broadly worked well, and if there is any time to be fielding a midfield without a ball-winner, it is at home against a League Two club.

Scholes return should not cloud the issue

Last week's column suggested that Manchester United needed a "runner" rather than a "passer" in the centre of midfield. The surprise return of Paul Scholes to United's playing staff clearly brings more invention than mobility to that zone, but with Sir Alex Ferguson so short on numbers in that he has been forced to deploy at least five players away from their natural position in central midfield, the more options the better. Scholes knows the system and costs nothing, making him a decent short-term solution, but he should not cloud the issue of what United need.

Michael Cox is the editor of tactics website zonalmarking.net. Read his new weekly column at guardian.co.uk