Cahill has come under heavy criticism from pundits and Chelsea fans for his role in Manchester United's second goal.
The England international was seen picking up Manchester United attacking midfielder Jesse Lingard in the area just before Ander Herrera's shot deflected past Asmir Begovic.
The strike came shortly after half-time and Chelsea could not recover from the psychological blow of falling further behind.
Speaking to Standard Sport, an angry Cahill said: "How can it be down to me? I just don't understand this.
"After the situation with Lingard happened, the ball has been cleared out of the area, come back in again, cleared again and then a shot has come in from the edge of the box.
"I was on the left hand side of (central defence), but the ball deflected off a couple of Chelsea players and went in. What could I have done differently?
"I always reflect on goals and will do so again, but I'm not sure what picking him up had on the goal. In hindsight I wish I hadn't done it, but that was the way I reacted."
The images of Cahill lifting his England team-mate to his feet looked like he was trying to help the Manchester United player in some act of sportsmanship.
But Cahill has explained that he was worried that referee Robert Madley was going to award Jose Mourinho's side a sport kick for his challenge on Lingard.
He added: "I just want to clarify things because people love to pick up on incidents that aren't really relevant in the game.
"All I can be is honest. My natural instinct was the ball came in and I grabbed him with my arm. I felt there was a slight chance he could get a penalty, it wasn't me being Mr nice guy by lifting him back up again.
"Listen, I'd do absolutely anything to win, from now until the end of the season. The pure instinct was worrying about the penalty and I wanted him to get back on his feet as quickly as possible so the referee didn't think otherwise.
"In hindsight it probably looks a bit silly on TV, but I can only react to my instinct and that's what I did. I wanted to make sure no penalty was given."