The Polish champions were thrown out of the competition for fielding an ineligible player in the second leg of their 6-1 third qualifying round clash with Strachan's old side.
The Parkhead outfit have now been given a second chance of landing a £20million jackpot and a slot in the competition's group stages after they were handed Legia's play-off round place.
But on Sunday, the angry Poles held a press conference and even released an open letter to the Hoops as they questioned the honour of the club's hierarchy.
They have demanded a rematch in order to decide who faces Slovenians Maribor but Strachan insists Legia will have to take their punishment.
"That's the rules," said the Dark Blues boss. "It's the same in golf. If it's a windy day and the ball moves or oscillates as you're addressing it, that's a penalty.
"Every sport has its rules and you have to stick by them. But most of us have all been hit by these rules somewhere along the line."
Celtic thought their Champions League hopes were over after sustaining a crushing 4-1 defeat in Warsaw.
It was just new boss Ronny Deila's third match in charge but when Legia blundered by playing the suspended Bartosz Bereszynski, the Norwegian was handed a reprieve.
Now Strachan has tipped the former Stromsgodset manager to bounce back from the pounding his team took in the Polish Army Stadium.
He suffered a humiliating 5-0 thrashing by Artmedia Bratislava in his first match as Celtic boss back in July 2007 but went on to become the first Parkhead manager since Jock Stein to win three Scottish titles in a row.
Deila's predecessor Neil Lennon, meanwhile, suffered European set-backs during his first full season in charge but lead his side to a famous win over Barcelona and the Champions League last 16 a year later.
"I'm still looking at the team-sheet to see how many of the team in Bratislava are ineligible," joked Strachan, whose side failed to progress despite a 4-0 win in the Parkhead return. "I will need to get Peter Lawwell to go over that just in case I'm due a bonus for getting through to the next round.
"But getting over a bad result like that can be done. Lenny had a poor start and did well and these things are sent to test you.
"Everyone in football will have their character tested but we wish Ronny the best of luck."
Speaking at Heriott Watt University as the third intake of youngsters were welcomed into the Scottish Football Association's Performance Schools system, Strachan also reflected on a summer that has seen three Scottish youngsters seal big money moves.
Dundee United's Ryan Gauld clinched a £3m switch to Sporting Lisbon, while Tannadice team-mate Andy Robertson moved to Hull for £2.85m.
St Johnstone's Stevie May has also landed a £800,000 transfer to Sheffield Wednesday but Strachan would rather see his nation's best talent stay north of the border.
"It would be better for me if we had the finances in this country that nobody would need to move," he said.
"Walter Smith told me four or five years ago that there were 70-odd players who had played in the Scottish Premiership that were now playing in the English Championship.
"If we had kept them here, just think what a fantastic league we could have.
"The trouble is if you develop good players, people want to buy them. Just look at Southampton. They do well then £100millions worth [of talent] moves on.
"That's what happens and what will always happen - the top club will come in and take your players.
"What I would like to see in years to come is Real Madrid, Barcelona, Man United buying our players again. That would be better for everyone."