Mahadik injured his ankle in the 31st minute when a Korean player stamped on his foot and was off the field till the last five minutes when India went all out.
Singh said Mahadik's absence resulted in players taking up unaccustomed positions.
"It was very disappointing. We played well in the first half, but our team's structure fell apart after the injury sustained by Mahadik just before half-time," said Harendra Singh, after India's 2-3 defeat.
"The team's structure could not be maintained and we had to use Vikram Pillay and later Arjun Halappa as sweeper-backs. Halappa is not used to playing in that position," Harendra said.
"The advantage went to South Korea, as we faltered with the structure of our game after a senior defender went out. It was only after Mahadik was brought back in the last five minutes that we looked to play in our usual structure," he added.
Harendra said the penalty-stroke awarded to South Korea, which resulted in the match-winner in the 56th minute, was unjustified.
"The massive blow for us came when the Koreans were given a penalty-stroke. The Korean striker had already taken a shot and was not in control of the ball at that stage. Even the goalkeeper was covering him at that stage, so the penalty-stroke award was harsh on us," he said.
Singh said it was disappointing to start the tournament with a defeat but he would take positives from the match as his side has come without at least half-a-dozen senior players.
"I'm obviously quite upset at the score-line, despite dominating the first session, but this match was good education for the youngsters in the team," he said.
Harendra is hoping that Mahadik recovers in time for Friday's match against Great Britain.
"I hope Mahadik recovers for tomorrow's match against Britain, which is almost their full strength and a lot of their players are from England's team whom we defeated in the Commonwealth Games semi-final. It's going to be a very interesting encounter," he said.