The Bundesliga outfit almost sent holders Real Madrid packing, winning 4-3 at the Santiago Bernabeu but departing 5-4 on aggregate in the last 16.
Di Matteo said he was happy and sad, proud of his team for their surprise victory but disappointed to be out of the competition.
"We played a great game and we dreamt of going through," the Italian said.
"We scored four goals against Real Madrid but we are not going through to the next round.
"We are happy, but also sad. We had a little bit of bad luck, we hit the post in both games."
A Cristiano Ronaldo brace had helped Real into a 3-2 lead on the night, but goals from Leroy Sane and Klaas-Jan Huntelaar put them under pressure in the closing stages.
Di Matteo said Ronaldo was the difference and backed Real coach Carlo Ancelotti, who is under increasing pressure.
"Cristiano Ronaldo made the difference in the first leg and also tonight," Di Matteo said.
"We made things difficult for Madrid. The atmosphere was not easy for them.
"Ancelotti is still a top, world-class coach."
Di Matteo praised his team and said Real's fans were entitled to their opinion, with supporters whistling and booing at their team after the game.
"Our team is young but they gave everything tonight and we feel good," he said.
"We scored four goals and played bravely. When Real Madrid play everybody expects a victory.
"There is a lot of pressure here and supporters have the right to show their opinion."
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