The former Celtic manager was speaking after the Hoops' defeat in UEFA Champions League qualifying.
There's pressure on Neil Lennon and the recruitment team at Celtic Park to invest in the first-team squad after their exit to CFR Cluj in UEFA Champions League qualifying.
It was a shocking and ultimately avoidable defeat.
Having lost a number of key players over the last 12 months, there's urgency to bolster a number of key positions.
Strachan though feels there's no need to appease the 'baying hordes' criticising the club currently.
As quoted by The Daily Record, he said: "Celtic don’t need to panic buy. They have enough. I really don’t know if they have to do too much.
"Do they want to go out and buy someone just to appease the baying hordes, more likely five or six moaners on the internet, or do they just calm down and know that they have enough?
"If there’s something super-duper out there, of course, they’ll do it, they’ve done that before. But they won’t be pushed into anything drastic."
With a left-back and right-back badly needed, for starters, to provide competition and cover, Strachan's comments come across as slightly out of touch with the realities at Celtic Park.
After the departure of Kieran Tierney, only Boli Bolingoli is available on the left flank and Lennon played a midfielder in the position on Tuesday night.
On the right flank Hatem Abd Elhamed looks a solid choice, but Lennon has been forced to use central defender Kristoffer Ajer as back-up in the position recently.
If the Hoops go ahead with the squad currently in place it will be a massive risk, both domestically and in Europe.
They are a few injuries away from having to play inexperienced players who don't have what's required to win trophies and cope with the pressures of a 'nine-in-a-row' bid.
It's understandable that Strachan would look to publicly defend his old club and captain Lennon, but he's mistaken if he thinks Celtic fans will accept poor recruitment before the transfer window closes.
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