Andriy Shevchenko praised the Ukraine fans who made their way to Hampden Park, after substitute Artem Dovbyk's dramatic extra time winner booked their Euro 2020 quarter-final place against England on Saturday.
Manchester City's Oleksandr Zinchenko opened the scoring in the 27th minute but Emil Forsberg levelled with his fourth goal of the competition two minutes from the interval.
In the first half of extra time Italian referee Daniel Orsata, with the help of VAR, sent off Sweden's Marcus Danielson for a high tackle on Ukraine substitute Artem Besedin.
The 10 men looked as if they would hold out for penalties but as the match edged into three minutes of added time, Dovbyk headed in a cross from Zinchenko from close range to send the Ukraine supporters, among the attendance of several thousand, wild with delight.
Boss Shevchenko, who will assess Besedin's injury on Wednesday, said: "First of all I would like to congratulate every fans' support of Ukraine for this historic moment.
"The players played for the supporters. We are really pleased.
"It was really hard to get here but our diaspora really supported us.
"The majority of those people work and I think they might have spent the last money they had to come to this game.
"We heard you, thank you very much for this support and greeting to the whole Ukraine, to our president for his support for the support of the whole Ukraine, we know that they were watching and supporting us."
Sweden head coach Janne Andersson said: "First half we had chances but they managed to get the lead. We equalised before half-time, and in the second half we had four really great chances including hitting the post and the crossbar.
"It felt we would score eventually, but unfortunately we didn't."
On the penalty, he said: "My colleagues in the stand told me it was a red card.
"It was a very experienced referee. I haven't seen it yet but I think it's probably right."
Asked about Ukraine's sickening late winner and his exchange of words with Shevchenko at the end, Andersson said: "We managed to keep them away well, but I thought we maybe should have kept it away.
"I was a little bit tired. I felt they were diving a bit towards the end, but I was complaining to the fourth official. He didn't agree with me."