Ukraine had countless chances to score and never gave up, but the 0-0 draw saw them end at the bottom of a Group E that had been on a knife edge, eliminated by goal difference despite having the same number of points as Belgium, Slovakia and Romania, who all advanced.
In the end, it came down to Ukraine's 3-0 defeat in their opening match to Romania, and a failure to wake up after the first goal went in, according to Rebrov.
"Everybody saw that we were trying to win this game, we were trying to create certain moments, there were enough interesting moments," he said.
"But we were playing against one of the top teams so it was very tough, unfortunately, we did not use the opportunities."
Rebrov expressed pride at the way his players responded in their 2-1 win against Slovakia and against a Belgium side on Wednesday packed with big-name talent.
For Ukraine, competing at a major tournament in a time of war was their biggest victory, he said.
"We showed the character of our nation, we are nearly 900 days in the war and I think today was very important to show the people in Europe, to show our people in Ukraine, that we are still fighting ... This very important for us to be represented here," he said.
"We didn't do well first game but you know in life you make some mistakes and then it's very important how you react, I think we reacted well."
Ukraine carved out a succession of opportunities in the first half and battled to the end, missing chances in the dying seconds. The players were devastated at the final whistle, lost for words as fans held their heads in their hands wondering at what could have been.
The team lined up before their supporters in a stand full of fluttering flags, raising their hands above their heads in choreographed applause.
"I saw the players, they unfortunately don't have emotions anymore," Rebrov said.
"We have a very young national team and I can see that they are optimistic about the future. Unfortunately today we need to live through this day and tomorrow we need to start working again."