Myles Lewis-Skelly, on debut, and captain Harry Kane scored for the 2-0 win on Friday evening.
“I think we had clear ideas on what we wanted to do and how we wanted to play,” said Bellingham. “We tried to stick to that as much as possible. I know it's difficult when you play against a team that sits so low and is so compact.
“At times the game takes you a different direction. You want to get on the ball and move them around but generally we stuck to the plan really well. We had a really good week of training and it's a good way to start the new era.”
The Real Madrid midfielder also had a word for England debutant Lewis-Skelly, after the Arsenal left-back scored on debut.
“It was a really good run and I managed to find the path of the run,” explained Bellingham. “He finished it really well and I'm really happy for him.
“An amazing first game and a really nice and well-taken first game and a win. He'll never forget it and we're really happy for him.
“When you come into the team, there are a lot of lads to help you. We hope that for him, he only has to worry about his own head and own coolness and obviously he has plenty of that. We wanted to do what we could to help him enjoy it and I think he did.”