Jarrod Bowen struck an equaliser for West Ham after Everton went ahead through Michael Keane.
Earning a point on his debut, Nuno said afterwards: "We have to learn so many things. It was a tough game. The reaction was good and overall we compete well.
"There are some positives, there are negatives but now it's about analysing and trying to find the right solutions. Our message today was very clear, it was competing as a team, being closer to each other and the boys did well. Overall, it's a good first game for us.
"In the second half, we started defending better. Everything starts from there. I think the team did well in that aspect. Things will come naturally and it's about taking the right steps forward.
"The boys are slowly understanding that a football match is also about how we close our own goal, how many chances we concede, these are things we have to work on."
Nuno added: "We have to build on that. Now it is about keeping it simple and trying to give the boys a good identity. We will get there in terms of identity and character but now it's keeping it simple.
"The clear message was how we have to approach the game. It is a tough place to come and Everton are a good team in a good moment."