Ferguson felt Carroll deserved a red card for his robust aerial challenge on De Gea from a West Ham corner right on the stroke of half-time.
Carroll escaped punishment for the foul on De Gea and the big striker insists there was nothing he could to stop himself colliding with the keeper as he challenged for the ball.
"I just went for the ball and obviously went through De Gea, but I just went for the ball and that's all it was," Carroll told Sky Sports 2
"I was running straight in trying to get the ball and couldn't stop at that moment, obviously the keeper has come and won it and I couldn't stop when I was flying through the air."
Carroll had a running battle with the United defence and also clashed with England team-mate Wayne Rooney in the build-up to the De Gea clash and he admitted he enjoyed the physical challenges in the game.
"It was great, a tough battle, I enjoyed every minute and getting stuck in, getting a few elbows and giving a few. It's all part of the game," added Carroll.
On his clash with Rooney he added: "It was a bit of friendly banter with me and Wazza,
Carroll admits he has enjoyed his loan spell at West Ham from Liverpool, but remains unsure where his long-term future lies this summer.
"I've loved every minute and the lads have been great, the fans have been excellent and I am just carrying on going until the end of the season," continued Carroll.
"We will just have to wait and see what happens."