Strachan is outraged that photographers pictured Keane hobbling out of training on Friday after suffering a hamstring injury. They also captured the reaction of the coach Tommy Burns.
He has vowed to ban cameras from future training sessions, while he also insists that predictions surrounding the length of time the former Manchester United skipper will be out have been exaggerated.
Strachan, who had watched his side move 10 points clear of Hearts at the top of the Scottish Premier League with a 3-1 victory at Motherwell, snapped: "If we had listened to the tabloid physios we would have been looking at four to six weeks. But to those that are qualified he could be out for seven to eight days.
"Some of the pictures had Tommy with his head in his hands so that'll be the last picture they get on a Friday."
Hearts' slip-up against Kilmarnock let Celtic establish their commanding lead but Strachan is refusing to rule the Edinburgh side or any of the chasing pack out of the equation.
"No it's not over, because everywhere in football there are examples that we cannot afford to take things for granted," he said, before heaping praise on his new centre-back partnership of Adam Virgo and Stanislav Varga. They came in from the cold to replace the injured Keane and the suspended Stephen McManus.
Motherwell's Jim Hamilton cancelled out Maciej Zurawski's opener with a contender for goal of the season, but the substitute Aiden McGeady put Celtic back in front before John Hartson secured the points.
The Motherwell manager Terry Butcher was understandably upset after being unfortunate to lose to Rangers at Fir Park a week ago. Butcher said: "Of course I am disappointed with that. Celtic scored the second and we squandered a great chance [from Scott McDonald] after that to make it 2-2."
Goals: Zurawski (17) 0-1; Hamilton (41) 1-1; McGeady (71) 1-2; Hartson (85) 1-3.
Motherwell: G Smith, Corrigan, Craigan, Kinniburgh (McLean, 84), Hammell, Kerr, McBride, McCormack, Foran, S McDonald, Hamilton. Substitutes not used: Meldrum (gk), Fagan, Maguire, Coakley, Reynolds, D Lee Smith.
Celtic: Boruc, Telfer, Virgo, Varga, Camara, Nakamura (McGeady, 62), Lennon, Petrov, Maloney, Zurawski (Pearson, 74), Hartson. Substitutes not used: Marshall (gk), Wilson, Wallace, Lawson, O'Dea.
Referee: C Richmond (Scotland).
Booked: Motherwell McCormack, Foran, Hamilton.
Man of the match: Virgo.
l Dado Prso came off the bench to score twice in the last minute to secure Rangers' 4-1 win over Livingston on Saturday. The Croatia international had missed nine matches with a hamstring injury. Heart of Midlothian's head coach, Graham Rix, admitted that his side's season could be in danger of unravelling after their 1-0 defeat at Rugby Park. He said: "We are second in the League and we're in the Scottish Cup, but many more performances like that and all the good work that's gone beforehand could be thrown away."