Iliman Ndiaye had Everton ahead via the penalty spot before Rayan and Amine Adli struck for the Cherries. The visitors' goals came before Jake O'Brien's dismissal.
Moyes told evertontv: "I've not got much to say, really. I'm disappointed.
"It's a game we could have won, possibly. It looked as if we might have done. It was a bit scrappy at times, but I'm just disappointed that we gave away two really poor goals. We also missed two or three (chances) ourselves, so we've only ourselves to blame.
"I think just after half-time... we started the second half well but it's only talk if you don't score – and we're not scoring enough."
On the spirit shown, despite the defeat, Moyes added: "The players have done a great job here.
"The results and performances they've got themselves in the league have been really good, so no complaints (over the spirit) at all."
