Ajax humiliated Madrid 4-1 in the Spanish capital en route to the quarters and the in-form Dutch side also claimed the scalp of Juve thanks to Tuesday's 2-1 second-leg victory in Turin.
Goals from Donny van de Beek and captain Matthijs De Ligt cancelled out Cristiano Ronaldo's opener and gave Ajax a 3-2 aggregate victory against the Serie A champions.
Barcelona-bound midfielder De Jong – who will join the La Liga giants next season – said it was more difficult for Ajax in Madrid, having lost the opening leg 2-1 to the three-time reigning champions.
"I do not know if this is the best match of our lives but it went well," De Jong told RMC Sport. "In Madrid it was harder because we lost in the first leg.
"Juve are very strong, very disciplined, we showed in the second half the team we could be. The coach asked the same things as usual, play high and play possession.
"Win the Champions League? We are in the semi-finals, we have a chance but we are not favourites. But of course, it's always possible."
Van de Beek, who equalised for Ajax before half-time, added via Veronica TV: "Everyone is going crazy, Ajax are in the semi-final!
"If we'd said that at the start of the season, people would've laughed at us. This is a fantastic result for the whole of the Netherlands.
"None of us will ever forget this night. To be honest, we were the better team in the first half too. Obviously, in the second half we were the far better team.
"I thought we should've won 4-1. When we were 2-1 up, I was already thinking ahead to the semi-final, trying to make sure I didn't get booked."