All three British clubs have drifted in Sky Bet's Champions League betting after Thursday's last-16 draw.
Manchester United were handed the toughest possible task as they were paired with Spanish champions Real Madrid, prompting their price to drift out from 10/1 to 14/1.
Arsenal will also have to defy the odds if they are to make the quarter-finals as they face last season's finalists, Bayern Munich, who they are 2/1 to progress past.
The Gunners were already considered outsiders for Europe's top trophy at 25/1 but have since been pushed out to 33/1.
Celtic are now the longest price of all 16 sides left in the competition at 125/1, with their chances of ousting Juventus rated at 4/1.
Juve are considered the main benefactors of the draw, with their price coming in from 12/1 to 9/1, while favourites Barcelona, who face AC Milan, have also had their price trimmed from 5/2 to 2/1.
Sky Bet's Chris Spicer said: "In drawing Real Madrid and Bayern Munich, the two Premier League sides have been handed the second and third favourites, so things could not have gone much worse.
"All three British sides are outsiders to make the quarter-finals now and we go 7/5 that none of them will progress, while a British winner is 11/1."