Ivanovic rose to head home in the final minute to give Chelsea a 2-1 win over Benfica in Amsterdam.
Fernando Torres had scored an excellent individual goal to put the Premier League outfit ahead before Oscar Cardozo levelled from the spot.
"This is one of the best moments of my career," said Ivanovic. "Winning a European final like this is a dream.
"I always said it is the team who win every title - not individuals. Even tonight we had some people missing through injury.
"But I am so happy. It is a pleasure to be part of this team. When you win one trophy, you should always want another. There is something within sport that keeps pushing you on.
"We have felt that a lot of times this season. We used it as extra motivation."
Torres added: "I am very happy, I could not wait and it was a tough game, and maybe Benfica deserved more, but maybe the individual quality made the difference."
Torres admitted that Chelsea were second best in the opening half.
He said: "The first half was not good enough at all - and we had to change our mentality to win a final and you could see a difference in the second half."
The Spaniard was again asked about his future at the club, and reiterated that he sees himself staying at Stamford Bridge.
"I signed for five years and I hope to stay at least for this time."