After Callum Wilson's first-half brace for the visitors, the hosts fought back after the break through a Marcus Tavernier penalty and an Enes Unal strike.
Nuno said, "Let me start by saying we had a two-goal advantage, but in the end when we went to our fans, the fans realised the effort of the players.
"It's a very tough place to come. The first half was us - we took advantage of the straight ball, of the second ball, we managed the tempo of the game, we managed to control Bournemouth, and we achieved a good lead.
"In the second half, Bournemouth did exactly the same that we did. They managed better the circumstances of the game, we couldn't go out, they put us against the ropes, they engaged five players in the last line.
"The boys were organised but were missing the pass to go out of pressure, to really hurt them with space, under tough circumstances.
"But the positive is that I think the team was resilient, was organised, was compact and was really committed.
"The fight was required from us, there's no other way, especially on a day like today, here at Bournemouth.
"It's a tough, tough (place), so it's a positive in terms of commitment, resilience.
"Something was missing, something that we have to work on and try to take and hold on to the kind of advantage. Not only hold on but try to punish teams when you achieve this advantage."
On Wilson, who was playing at Dean Court for the first time since he left for Newcastle, Nuno added: "I'm very happy that Callum is giving us these moments.
"He knows how to move himself in the box and the team has to realise and take advantage of it."