Bale was speaking after coming off the bench in Madrid's 6-1 hammering of Galatasaray in Istanbul in the 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."