Jadon Sancho started for the visitors and opened the scoring five minutes after half-time.
The Englishman pounced on poor control from Jorginho to race clear and slot the ball past Edouard Mendy.
It was a shock for Thomas Tuchel's side, who had dominated possession up until that point, but they were back level only 19 minutes later when Jorginho hit the back of the net.
Ronaldo replaced Sancho in the second-half but cut a frustrated figure as he was booked for dissent and stormed off straight after the final whistle.
They will be hoping to bring that solidity to Thursday's clash with Arsenal at Old Trafford.
Speaking after the game, Carrick said he was disappointed United were unable to hold onto their lead.
"I'm disappointed, actually," the Englishman said. "When you're in front in a game like this, to have it taken away from you like it was is disappointing.
"Immensely proud of the players, immensely proud of the whole group. All week, [we've been] in a difficult situation and trying to make the best of it.
"[We] can't hide from that, it's been tough at times but we've made the best of it and I'm immensely proud of the response and the way we've gone about it this week. We came here to win the game, we had a plan, we were positive in our mindset and in our attitude for that, so we're a little bit disappointed, I can't lie."