Bale was speaking after coming off the bench in Madrid's 6-1 hammering of Galatasaray in Istanbul in the UEFA Champions League.
The Wales international came on midway through the second half and played his part in two goals as Cristiano Ronaldo claimed a hat-trick.
But Bale had no concerns about starting from the bench and was just happy to be back playing in the world's biggest club competition.
"It is amazing and a big reason why I joined such a big club was to be playing in the biggest competition in the world and it was great to get out there tonight, get the win and a good start," he told Sky Sports.
Bale surprisingly made his debut from the start against Villarreal last weekend, but he knew he would not start two games in a row due to his lack of pre-season prior to his world record move.
"I spoke with the manager and I had no pre-season whatsoever, I have trained seven or eight days, had 30 minutes for Wales and 60 minutes on the weekend so it was all about easing me in, and I felt good when I came on and I contributed," he continued.
"It is a different situation not to have a pre-season and it is a bit difficult, but I am feeling like I am getting there, getting minutes on the pitch and it is all about game time and building myself up."
Bale says he is already feeling part of the squad and added: "I think all the boys have made me very welcome and I have settled straight away and I am enjoying my football and want to crack on now, get my fitness up and play a lot more games and have a good season."