The Jamaican, City’s leading scorer with 14 goals in as many matches this season, was ruled out of City’s 2-0 win over St Polten after yesterday’s training session.
Lily Murphy was drafted into the side as Shaw’s replacement and marked her first senior start with the opening goal, before Kerstin Casparij added a second on the hour.
But there was a further injury concern in the first half against the Austrian side when captain Greenwood was stretchered off after a heavy collision.
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Taylor admitted it was too early to provide a full assessment on Greenwood but added that Shaw was unlikely to feature against either Everton or Barcelona before the Christmas break.
“I’m not too sure, we’ve had multiple scans on the area that she has the issue with, we’ll have to wait and find out,” the boss said.
“I don’t think we’ll see her until the new year which is a shame for us because she was in a really good vein of form.
“The players did really well tonight, I have to give great credit. I really admire how we got the job done in difficult circumstances.”
On Greenwood, the boss added: “We’ll have to assess. Alex doesn’t normally come off unless it’s an issue, hopefully it’s nothing too bad because we could do without it, we’re missing so many players.
“We lost Bunny yesterday, then there’s the likes of Naomi Layzell missing, Lauren Hemp, Vivianne Miedema, Laura Coombs at the moment we’re really up against it player-wise.”
The boss also heaped praise on teenager Murphy, who was named Player of the Match on her first senior start.
At just 18, the forward opened her City account having signed her first professional deal last week, tapping home Aoba Fujino’s cross to hand us the lead.
One of Murphy’s greatest assets is her searing pace and while she still has some plenty to learn in her young career, Taylor says her speed is unparalleled.
“It’s exciting because we’ve got someone there with pace that I’ve never seen in the game, and what you can do with that is incredible.
“For me it’s about trying to unpick some of the stuff she’s been doing and get as much technical rhythm into her.
“If you have that pace in the team it causes real problems for most teams.”