Cahill clattered into the Germany midfielder in the 56th minute of the Group D encounter, staring in disbelief as Mexican referee Marco Rodriguez brandished the red card.
"It was a devastating blow to me and my career," he told reporters, choking back the tears.
"I think I merited a yellow card, the referee's decision was too harsh.
"Schweinsteiger made a meal of the incident. That's why the referee issued a red card. I can understand him. It was to their advantage. That's football."
"I think all the credit goes to Germany," he added. "They played well, they dominated us throughout the encounter and they deserved to win. But the score was too hard on us."
"They were the better side," he said. "Yes, Tim had a red card but he cannot be held responsible for us losing the game. It was a collective responsibility.
"Now we are left with no choice but to win the remaining two games in this round, it's not going to be easy but we'll have a try."
