The defender slotted in alongside Connor Goldson in the second half as Gers ran out 4-1 winners over Dundee United.
But the concession of a goal – despite the Light Blues being 4-0 up – was a major talking point for the defensive unit after the match.
Speaking to RangersTV, Simpson explained: "I am delighted to have made my debut and the most important thing is three points.
"But, especially from the back four and goalkeeper's point of view, we are disappointed to concede a sloppy goal towards the end there as clean sheets mean a lot to us with the standards we set here.
"So I am pleased, but also a little disappointed.
"The standard is very high here. Just come coming in to training, everyone is on it here and not even just on the pitch, but around the training ground and the gym, the standards are set very high and everyone is expected to do everything they can to be ready for matchday.
"So I have been very impressed so far. I feel like the more I learn how the team plays and the more gametime I get, the more comfortable I feel and I think I had can add something.
"I feel comfortable on the ball and I want to bring the ball out and be aggressive defensively on and off the ball.
"So I definitely feel like I can add something to the team seeing the way they play."
Simpson was on the bench for Thursday’s incredible 4-3 win away to Royal Antwerp, and he’s hoping to be involved for the return leg this coming week.
He continued: "Everyone wants to play European football when I was a kid so it was exciting to be able to do that.
"It ended up being a crazy game really so it was a positive to come away with the four away goals to bring it back here and I am looking forward to the game on Thursday and hopefully we can go through."