The England midfielder, whose loan switch from Manchester City was arguably the most high-profile deal in this transfer window, inadvertently set up Dominic Solanke to score with less than three minutes gone.
Fortunately for West Ham, a James Ward-Prowse penalty in the second-half was enough to secure a 1-1 draw.
“It’s not a goal we concede too often and it gave them a leg up,” said Moyes.
“Then we had to perform and we weren’t at a level to do that. It wasn’t as good as it should have been.
“Kalvin’s fine, he got best part of 70 minutes in. I said before we might have to go a bit gently with him.
“I thought as the game went on he was starting to get better, but he was a bit slow at the start and in getting into the way we play.
“I’m happy with a point but not happy with the performance. We got back in the game and I didn’t think we performed well after that either.
“It looked as if we had had 10 days off tonight, like we’d had a holiday, the players looked leggy.”
Moyes was annoyed that West Ham, for the second time this season, had to play on transfer deadline day.
Fornals was still in the tunnel at the final whistle with Moyes in the dark over his future less than an hour before the deadline.
“It’s strange day to have a game and also the deadline,” he added: “We were planning to have Pablo involved tonight. He might still be here, who knows?
“I think it could have been wrapped up last night. It’s our own fault in this country we do so many deals in the last day. This window has been a really slow burner and we’ve had it on a game night.”
Cherries boss Andoni Iraola said: “There is a part when you have to value the point, but I think if any team deserved to win today it was Bournemouth.
“We were 1-0 up and had very good chances but if you don’t punish these teams it can happen.”