A tangle with Manuel Akanji left the striker on the turf and he initially slapped the ground in frustration as fears over a fresh injury grew.
Rashford received treatment and continued but looked a bit uncomfortable for much of the second half.
“Just a little knock,” he confirmed to BT Sport post-game.
After Bruno Fernandes’ leveller, Rashford popped up to tap home Alejandro Garnacho’s cross to secure a dramatic derby comeback late on on Saturday afternoon.
He continued: “In games like this you just have to try and push through, thankfully I managed to do that - scoring the goal at the end and winning the game.
“That’s what we set out to do, that’s always the aim with every game. This one is obviously a little bit special but pleased to have the three points and continue winning at Old Trafford.”