The Argentine kept his place in the United line-up as Carrick made two changes to the side that started in the Spanish capital, with Harry Maguire and Amad Diallo coming in for Ayden Heaven and Marcus Rashford.
However, he did not appear for the second half as he was replaced by a returning Noussair Mazraoui before joining the rest of the Man United substitutes on the bench.
Carrick has since provided an update, confirming Martinez picked up a knock.
“He felt his thigh a little bit,” the Man United boss told reporters.
It now remains to be seen how serious the thigh issue is, though Martinez could be a doubt for Man United’s next fixture against Como in the Champions League on Wednesday evening.
Lisandro Martinez played 45 minutes against Leeds
Getty
While United’s draw with Leeds has extended their winless run to six games across competitions, Carrick believes the point was a step in the right direction.
"It definitely was [a step in the right direction]. If there's any weakness, it gets found out today,” he said. "I could feel before the game that the players were ready for it.
“It wasn't perfect. Our confidence isn't sky-high, but the players were trying to do the right things.
"In moments we looked really good. Defended really well as a team.
"Credit to Daniel and his team. They are a very good team. They test you and ask alot of questions. If you are not ready for it you get found out and I thought the boys stood up to it."