Victory at Eintracht Frankfurt on Wednesday saw Spurs finish fourth on the group table.
Gray said after the 2-0 win: "It's a massive relief and something that we're really proud of, to finish top four in the Champions League with the best teams in the world. It's where we want to be.
"To have two fewer games in a season can be massive and especially with the tough fixtures that we've got coming up, it's nice to be able to prepare a little bit more for those games.
"It was a little bit of a slow-paced game, only a few transitions, but once we got in their half we knew they were going to be difficult to break down and that it was going to take quite a bit of time, especially when they had 11 men behind the ball. But we got there in the end.
"It's every kid's dream and I'll never take it for granted, playing in the Champions League. Some players never get to do that, and I'll be always very, very proud to be there."