The point still leaves West Ham inside the bottom three, but maintains their recent momentum.
Nuno said, "It was a tough game, we knew that Bournemouth is a good team, I think we played a good game.
"The boys competed really well, we were organised, we didn't allow too many chances in terms of Bournemouth, the way they play.
"Of course, when the game opened up, it could go both ways, but that is the risk that we acknowledge and we wanted to take.
"But overall, it was a good performance, and I'm sad about the result because we almost got there.
"The chances that we created could have been different, but I’m proud of the way the boys worked.
"There are many things that we are improving and today we showed that we are resilient, we were compact, we didn't allow chances, we had good possessions.
"Thank you to our fans that, again, until the last minute were supporting us."
Taking our chances
Nuno says the Hammers were unfortunate not to make the most of the chances created.
He continued: "I think it's about being able to always really start well and score first. All the chances at the beginning of the game are ours. That was the message, to start strong on the front foot, and the boys did it.
"Unfortunately, it didn't happen, but we keep the composure, we keep organised, knowing that when you play against Bournemouth and you lose your balance and the game becomes like a basketball game, it becomes really dangerous.
"I think we are improving defensively, I think we are improving. Recently, we've been showing that it's not all about the back line. It starts with our striker, our shape, our organisation, reducing gaps, closing the lines, pressing really strong.
"It takes a lot of energy from ourselves, we press high, we chase. It's about that, it's not always trying to contain, but the way we press, the boys are working really hard.
"Like I said, it's not about our goalkeeper and back line, it starts with our striker."