The young duo started for the Magpies in their 1-1 Europa League draw with Atromitos in Greece on Thursday night and both hailed the experience after the game
18-year-old Bigirmana, who signed for the club from Coventry in July, made his debut in midfield whilst Tavernier was handed only his second start for the Tyneside outfit in defence.
After the game, Bigirimana told the club's official website: “I never could have dreamt that this would be happening so quickly for me.
"As I always say, I just thank God for blessing me with all these opportunities and I’m just so grateful to be part of this adventure.
“The performance of the boys was good, it was a great game, a great debut and it is a joy.
“It was difficult conditions, with the heat and the pitch, but we are going to have to get used to these sorts of places in Europe. It’s a great experience for us to play on different pitches and in different conditions."
Tavernier, 20, was at fault for Atromitos' opening goal, as the right-back allowed Denis Epstein to get beyond him to score.
However, the defender underlined his determination to learn from the experience and revealed his pride at featuring in the match.
“I’ll go away and I’ll get a copy of the game and I’ll look through it and analyse myself," he added.
“I’m really honoured to have played in Europe and hopefully I’ll get better and better from here.
“Obviously it’s a much higher level than I’ve been used to. In the European game, there are different types of players that you come up against so it’s always a new experience to come up against them.”