For only the fourth time in their history the Reds scored five in a European away tie, the last of which came against Finnish side Haka in a 2001 Champions League qualifier.
Jonjo Shelvey, a 67th-minute substitute, stood out with two strikes while 19-year-old Andre Wisdom marked his senior debut with a header and Sebastian Coates and an Juhani Ojala own goal rounded off the scoring.
Liverpool looked fragile as they slipped from 2-1 up to 3-2 down after Ojala and Gonzalo Zarate had added to Nuzzolo's first-half equaliser.
With the first team having scored just nine goals in eight matches Rodgers' second-string, which included three debutants, found scoring much easier.
"We have come away with a young team into a European game and I want to talk about the five goals we scored which were absolutely magnificent," said Rodgers, who was happy to overlook the errors which saw them concede three.
"Of course we could have defended better and there is no question the three goals we gave away were disappointing.
"But to draw positives from tonight [Thursday] the young players were so courageous and brave to play and show that confidence, and my senior players were very much together and kept the young guys going.
"All round it was very pleasing. It was a chance for the young players to seize that opportunity to play and I think they did that for sure.
"We need to be better in certain areas but I think it is a night of great pride for the club and certainly me as a manager.
"To play like we did and get the goals we did was quite fantastic.
"It was a great [Coates] header from a terrific ball in and for Andre Wisdom, in his first game for Liverpool and especially it being in Europe, he scored a wonderful header."
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On the eve of the game Rodgers had called for his younger players, the average age of his travelling squad was 21, to seize their opportunity.
He spoke about not having the talent but the right mentality and he felt they showed that.
"One of the most pleasing things was we were in front and then to go behind at this level can be difficult," he added.
"But it shows you the togetherness of the group because you don't win games by that margin on quality alone, you need to have the personality and the determination and I think you have seen that in bucketloads tonight [Thursday]."
Rodgers also had praise for Shelvey, making his 45th appearance for the senior side, and predicted a bright future for the England Under-21 international.
"I felt it was the time of the game we needed him really," he said of Shelvey's second-half introduction.
"It worked well for us because once we got the equaliser they went to more 4-4-2, it gave us the extra man in midfield and we were able to dominate that bit more.
"He has been outstanding. He is still only 20 years of age and is developing and growing all the time and you saw his confidence when he came.
"The (first) goal we worked it very well and he did what he can do very well and I think he will be a big player for Liverpool."
Young Boys' coach Martin Rueda bemoaned the errors by his side, starting with a comical fourth-minute concession when Dusan Veskovac headed against team-mate Ojala to beat goalkeeper Marco Wolfli.
"Of course it was a bitter end and it is a pity but when you make that many mistakes - we gave away four goals - there was not much we can do despite scoring three against them," he said.
"We made too many individual mistakes and that cost us the match.
"If you make a mistake you immediately get penalised at this level."