Juve have won the Italian top flight for the last three seasons, but were unable to progress beyond the UEFA Champions League quarter-finals in 2013 and went out at the group stage this time around.
The Turin giants made it to the semi-finals of the UEFA Europa League before losing to Benfica and Lippi, who managed Juve for eight years over two spells, thinks they have work to do before they can compete with the continent's elite sides.
Lippi, now in charge of Chinese champions Guangzhou Evergrande, has stressed the importance of patience as Juve attempt to end their 18-year European trophy drought.
"Before becoming important in Europe you must win in your country," he told Perform.
"In Italy, Juventus showed they are the best team and it's not true they don't have opponents as this season they faced a really strong opponent like Roma who had an extraordinary season.
"However, Juventus were even better. In the last three seasons Juventus has improved a lot after a few bad years due to several things. (Antonio) Conte was very good at creating an important squad.
"They are now aware of their strength and they need to continue their growth at international level."
Juve were unable to see off Jorge Jesus' Benfica outfit over two legs, having been eliminated from the Champions League in controversial circumstances.
The Italian club were less than pleased when they had to replay their game with Galatasaray due to adverse weather conditions a day later on a difficult surface - with a late Wesley Sneijder goal sending them out.
Lippi is confident Juve's fortunes will change in Europe with more Champions League campaigns under their belt.
"Juve need three, four or five wins at international level," added Lippi, a five-time Serie A winner with the club.
"They are already among the best eight to 10 best in Europe but not among the best four to five such as Barcelona, Real Madrid, Bayern Munich and Borussia Dortmund.
"They need a few important wins to gain belief and self-confidence."
