"We made a mistake," Collina said. "I wish we hadn't made the mistake but we did. Referees are human beings and human beings make mistakes."
England defender John Terry made a goal-line clearance in the decisive group match in Donetsk on Tuesday, but replays showed the ball was over the line. England led 1-0 at the time.
Collina said Hungarian referee Viktor Kassai and his team of assistants would play no further part in the tournament, but no blame was attributed to the referee.He said Kassai would have found himself under too much pressure if he had stayed.
"Kassai is one of the best referees in Europe," Collina said.
Collina and UEFA executives faced hostile questioning about Tuesday's decision and the use of goal-line technology, which is being tested by FIFA.
UEFA said that of 302 close decisions made by referees in the 24 matches so far, 289 of them were correct and 13 incorrect, a 95.7 per cent accuracy rate.
"That's a huge result, even though we must still improve," Collina said.
Additional assistant referees, a UEFA experiment to try and improve refereeing decisions, had contributed to 16 referees' decisions at the tournament and 15 of them were correct.
"One was wrong," Collina said. "It was a human mistake made by a human being. Of course, it would be better if this was not the case."