On his debut, the 20-year-old put up an eye-catching display to help his side to a 3-0 home triumph in the Dutch Eredivisie.
He was voted Man of the Match by fans of the club after the game, his influence shown in his involvement in the sequence of play leading to the first two goals.
"I am very happy with my performance, but the whole team was strong, so that included me," Kudus told NOS.
"I want to compliment my colleagues. I heard yesterday that I was going to play, so I had to prepare well. The boys are good to me, it's like family to me here.
"I can play in different positions, both in attack and in midfield. You never know where you will end on the field. I'm ready for anything. Normally I play more in the front.
"The goal is to win as much as possible with the team. Everything individual will come afterwards."
Kudus joined Ajax in a five-year deal reportedly worth €9 million, signing from Danish outfit Nordsjaelland in July.
"I think he's great to see," Ajax coach Erik ten Hag told FOX Sports after the match.
"He is very active and dynamic and can play football with very high intensity.
"When Kudus gets the ball, he often does something good with it. He was also good defensively. He took a lot of balls.
"If he still learns to choose a better position in our system, then it will be a very nice player for Ajax."
After a bench role in the opening Eredivisie weekend, Kudus was handed a starting spot for Sunday's matchday two fixture owing to the absence of Ryan Gravenberch, paired alongside Edson Alvarez and Quincy Promes in midfield.
"Of course I can take him out [back to the bench], why not?" Ten Hag said, in context of the team dynamics should Gravenberch return.
"He has done a lot of good things, but there are also points for improvement, such as taking position. But the more he plays, the easier he learns to choose the right position.
"Of course Kudus can also play with Gravenberch. But did you see how many balls Alvarez took today? And how many he was on his way to be playable? We are going to play a lot of games this year and we will need all the players."
Kudus scored 11 goals in 25 league appearances for Nordsjaelland last season.