Benfica went through 4-2 on aggregate and Jardel felt that, after the nervy opening stages, his side fully deserved to reach the Europa League quarter-finals.
"We had a goal in mind, which was to qualify," UEFA.com quotes Jardel as saying. "We managed to win a match that we knew in advance would be very difficult.
"Bordeaux are a very strong team, but I was fortunate enough to score the first goal and things were a little bit easier for us after that. We were calmer after the goal and completely deserved the victory.
"The coach has been very good in how he's rotated the team. He gives minutes to all the players and all my colleagues are up to the task. We have a great team and we are aiming to win every competition we're involved in."
Jardel has made 18 league appearances for Benfica since joining in 2011.