Brophy pulled up just before the half-hour mark with his side already trailing to goals from Aberdeen duo Marley Watkins and Christian Ramirez.
Goodwin, reflecting on the injury to one-cap Scotland striker Brophy ahead of matches against Hibernian, Celtic and Rangers, said: "It looks like a hamstring.
"He will probably miss two or three weeks which would see us expect him back after the winter break.
"It's too early to call just now – we'll send him for a scan on Monday.
"It's a concern to lose any player and Eamonn is a key player for us, but every team has to deal with injury and suspension. That's why you build a strong squad."
Squad depth was also something Aberdeen boss Stephen Glass touched on after his side won consecutive league games for just the second time this term leaving them in sixth place.
Glass has not been afraid to make big calls over form, including dropping club captain Joe Lewis earlier in the season when he hit a rocky patch.
"He was brilliant," Glass said of his goalkeeper. "He had a couple of big saves in the first half, and I remember one in the second as well.
"It was a good performance from the big man, and he's been back to his best the last couple of weeks. Like them all, that needs to continue.
"There's a lot of competition here, so it's important the boys are on their game."
Former Don Curtis Main replaced Brophy when he limped out of the action and on the match itself, Goodwin said: "Aberdeen were a real threat all afternoon. Their front four were terrific. It's the first game in a number of weeks where I've been able to say 'we were well beaten by the better team'.
Full-back Scott Tanser grabbed the goal that briefly gave the Buddies a glimmer of hope at 2-1 down.
But Watkins and Ramirez each netted a second goal to wrap up a comprehensive Aberdeen win that leaves Goodwin's men without a win in eight games and lying in eighth place.