The Light Blues were outstanding to defeat the Eredivisie outfit on their own patch to send them through a play-off round tie with Turkish giants Galatasaray next week.
Speaking to RangersTV afterwards, the skipper said: "We are delighted to go through to the next round - it is what we wanted to do when we came here.
"We knew it was going to be a tough game - they have very good attacking players and with their combinations around the box, we knew it was going to be tough.
"But we have got two brilliant 'keepers and Greegsy [Allan McGregor] has stepped up tonight to pull off some unbelievable saves that kept us in the game.
"He would have been my 'Man of the Match' for keeping us in - we won 4-0, but he kept us the clean sheet which we are delighted with.
"It was maybe a bit of a slow start - I know we were 2-0 up in the first half but we knew in the second half we had to be more disciplined with our shape, which we were.
"Then we knew we were going to create chances, and thankfully we did.
"From front to back, we did unbelievably in the second half with our shape. We always have really good shape in European games and also domestically in our banks and we all go together and press together to win the ball back and set traps.
"I thought we were fantastic in the second half and credit to all the boys."
On his 50th goal, which came from the penalty spot, Tavernier smiled: "It means I get to take the top home and Jimmy [Bell] has to do me another top! We had a little joke inside after the game.
"It is incredible for myself to get to 50 goals as a right-back. The gaffer has put faith in me to put me on penalties, and thankfully it went in the back of the net.
"But like I always say, if I can help the boys in any way possible in a game with assists and goals, then I will do that, but tonight I am more pleased that we got the clean sheet and we are through to the next round."
Tavernier also grabbed an assist tonight from a corner which Connor Goldson nodded home, and he explained on that: "Credit to TC [Tom Culshaw] - he always gets us on the training ground working on our set-pieces and it is down to our big men at the back to get the head on it.
"Connor was the first corner we had tonight I think, and he got his head on it brilliantly. Then Fil got a goal as well which came from the second phase - they are big assets for us and hopefully that will help us throughout the season."
WATCH ALL OF TAVERNIER'S 50 GOALS HERE
Gers face a quick turnaround before facing Motherwell at Fir Park on Sunday. Tavernier said:"We have just got to recover now - get food in us and work with Jordan [Jordan Milsom], the physios and Disco [Davie Lavery, massuer].
"We know Motherwell will be a tough game, but like we have shown tonight, if we can put the same performance in, then we want to come away with three points."
Post match highlights, the full game, and 90 In 90 will all be available to view on RangersTV for subscribers HERE.
Rangers TV Monthly - Standard (£6) - Join now to watch exclusive RangersTV content. (Excluding Live Video, Including Live Audio)
Rangers TV Annual - Standard (£60) - Join now to watch exclusive RangersTV content. (Excluding Live Video, Including Live Audio)
CLICK to subscribe to our official YouTube channel and never miss another video: HERE