Middlesbrough 0 Manchester City 1: Strachan buoyed by 'refreshing' aspects of beaten Boro's display
This defeat also made it five defeats in the last six and provided further evidence of the need to strengthen his squad.
He was able to field striker Marcus Bent only after he agreed to extend his stay on loan by a fortnight, handed teenager Jonathan Franks another start, and once again used 16-year-old Luke Williams as a substitute.
However, he lost star man Adam Johnson, who has been repeatedly linked with a January move away from Teesside, to another hamstring injury.
Strachan said: "There were things in there that were refreshing.
"I saw players who want to play for the club and play for their team-mates, and I must now ensure that I bring more players along like that to help these guys that are doing this thing at the moment by digging in and trying to play and working hard and giving 100 per cent.
"I must find more players like that, who think this is a smashing club to play for and want the respect of their team-mates."
City's victory, their third in as many games since new manager Roberto Mancini's arrival, was secured by Benjani Mwaruwari's 45th-minute strike.
With Craig Bellamy, Carlos Tevez and Gareth Barry sitting on the bench, the visitors enjoyed the better of the first half and went close through Pablo Zabaleta and Martin Petrov.
However, it was Petrov who eventually unlocked the door on the stroke of half-time, sliding Benjani in to beat goalkeeper Danny Coyne from the edge of the area.
Boro responded gamely but never really threatened to trouble Shay Given in City's goal, and the Barclays Premier League side might have won more comfortably had Tevez, three times, Bellamy and Petrov made the most of second-half chances.
Manchester City defender Dedryck Boyata, 19, was drafted into Mancini's starting line-up after being told to cancel a planned trip back to his native Belgium over the festive period.
Having spent the previous two games of the Italian's reign on the bench, he played a significant part in a third successive clean sheet.
Belgium Under-21 international Boyata said: "I was due to fly home on Christmas Eve, but then I was told I had to stay back to train, so I was a bit upset at first. But I have been training with some fantastic players every day since, and now to make my debut is a fantastic feeling."
Middlesbrough: Coyne, Hoyte, Riggott, Wheater, McMahon, O'Neil, Rhys Williams, Arca (Luke Williams 70), Johnson (Emnes 32), Bent, Franks, Emnes (Yeates 57). Unused substitutes: Steele, Shawky, Grounds, Bennett.
Manchester City: Given, Richards (Barry 46), Garrido, Sylvinho, Kompany, Zabaleta, Petrov, Weiss (Bellamy 74), De Jong (Tevez 46), Mwaruwari, Boyata. Unused substitutes: Taylor, Vidal, Trippier, Tutte.
Referee: Stuart Attwell (Warwickshire).
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