The Saints cruised to a 3-0 derby success on Sunday, with Pompey boss Harry Redknapp bemoaning his lengthy injury list after the defeat.
Pompey have a catalogue of casualties and the absence of several key players has seen Redknapp's troops slide in to the relegation zone.
But Strachan feels Pompey are not a special case in being afflicted by injuries and has called on Southampton's fierce foes to quit moaning.
"We've had injuries before," stated Strachan. "We've just kept our mouths shut and got on with it.
"Last season I was without Tino Delgado, our record signing, and Marian Pahars, our top scorer from the year before, for the entire campaign.
"But I can't remember any sympathy coming my way. Nobody said 'Oh what a shame for Southampton'.
"So don't ask me to feel sorry for others now."
Redknapp insists his injury situation is so dire that he will be forced to raid the transfer market when the window reopens in the New Year, particularly as he will lose two more players to international commitments.
"I'll be looking around for new faces on loan or free transfers as our situation will be even worse when Amdy Faye and Yakubu Aiyegbeni go to the African Nations Cup," said Redknapp.
"People can say I'm looking for excuses or whatever. But the fact is I had six of my best 11 missing on Sunday."
Meanwhile, Saints defender Garry Monk has extended his loan spell at Second Division Barnsley by a further month.
