Alcacer joined Dortmund on loan from Barcelona late last month and his debut on Friday was a successful one.
The Spain international was involved in Marius Wolf's goal and later struck from 20 yards to seal Dortmund's 3-1 win, after Abdou Diallo's opener was cancelled out by Sebastien Haller.
Favre said the 25-year-old still needed time, before revealing Alcacer hurt his ankle late at Signal Iduna Park.
"He hasn't played all that much recently. He needs time to get to full fitness," he said.
"We're not sure exactly what happened, but at the end of the match he unfortunately felt some pain on the back of his ankle."
Favre was pleased with the result, which took his team to the top of the Bundesliga table with seven points from three games.
''They were a tough team to play against. The lead we took in the first half wasn't entirely undeserved but we were a bit lucky nonetheless. Although we controlled the match I wouldn't say we dominated it," he said.
"In the second half we were really eager to get the score to 2-0 as soon as possible, but we had a lot of trouble keeping the ball and controlling the match against the opposition's pressing game. We lost patience and that's what cost us our 1-0 lead.
"The substitutions gave us a sense of vigour. The goal which took the score to 2-1 was a really nice, well-worked goal. That's when the team was firing once more.
"We're really happy with the win."