Armando Sadiku was "hugely emotional" after his goal earned Albania a first win at a major tournament while coach Gianni De Biasi was hungry for more.
Sadiku's header two minutes before half-time clinched Albania a 1-0 win over Romania to finish third in Group A, potentially earning them a place in the last 16.
Sadiku told uefa.com: "It is, of course, hugely emotional. We've already achieved our goal and for that we are very happy. I am very satisfied to score but the credit goes to the whole team.
"I can't describe [the moment I scored]. It was very emotional. A very happy moment to see all the Albanians, to make them happy and see them celebrating. For this I am very pleased."
They will have to wait to see whether they progress as one of the four best third-placed teams.
De Biasi said: "I'm sure we gave huge joy to the Albanian fans. Not just the Albanians in Albania, but Albanians who live around the world.
"We contained a team that has quality and strength and that conceded just two goals in qualifying. We got there with heart and quality. We played with our heads and with mental strength.
"We will have to prepare as if we'll be playing on Friday or Saturday, so we'll have five or six days. We'll watch the other games and get ready.
"If we stay, we can cause trouble for other teams - even big teams. I think we grew in confidence tonight. "
Captain Lorik Cana added: "It's an incredible feeling. The guys in the team have sacrificed so much in these three matches. They gave so much of themselves, and I believe we deserved it and we have earned this reward.
"Desire, the heart that we have, the sacrifice - that's something incredible in our team."
Romania, the first country to bow out of the tournament and who last lost to Albania in 1948, went in search of an equaliser in the second half but despite hitting a post through substitute Florin Andone, they rarely tested Albania goalkeeper Etrit Berisha.
Coach Anghel Iordanescu said: "A loss is a loss and we're really sorry for what happened. Because of a mistake in our defence, we conceded a goal.
"Do I think we deserved to qualify? Yes and no. If you don't get a win, you don't deserve to qualify.
"I said yesterday that this was the game of a generation, and it's true: qualification would have been a reward for this generation. They did everything they could to qualify."
Source: PA
