Evanilson's double for Bournemouth sandwiched goals for West Ham from Niclas Fullkrug and Jarrod Bowen.
Potter said afterwards, "It was a game that went back and forward and changed.
"I thought the start of the game, we were OK without being brilliant against a tough opponent that you're always on a bit of an edge against because they've got such physicality and speed on the transition.
"We weren't brilliant first half and I think the second half of the first half tailed away from us too much. They were probably better than us there and then obviously to concede, you're filled with a disappointed feeling.
"And then second half, after the substitutions, we scored and then it was a fully committed, fully focused performance.
"I was delighted for Füllkrug because I think he had a real impact. You can see what he brings to the team.
"And obviously I was happy for Jarrod as well to score, and at 2-1 you hope that you're going to stay there, but a soft free-kick, I think it was, and then we haven't defended the action very well and then it's a point, like I said.
"I think it's a hard-earned point that's probably fair over the course of the game."
On Fullkrug's overall performance, Potter says the Germany striker showed what they've missed while he's been sidelined with injury.
The Hammers manager continued: "Sometimes in the Premier League, it's not easy to go from the goalkeeper through the team to attack and create stuff and I think Niclas gives us that out ball.
"He gives us a focal point. He gives us a chance to get second balls. He gives us a chance to attack quicker, a bit more vertically.
"We're just managing him back to full fitness and we have to be patient with him.
They were both really good headers and like I said, I’m pleased for both of them in different ways because Jarrod's been working really, really hard so he'll be the better for a goal.
"Probably the last two or three goals we've conceded have been a bit cheap from our perspective, so that's something we have to obviously keep going at.
"We scored two but we've conceded two and chances are we've probably conceded a few more than we'd like.
"But that's also something I keep speaking about before – it's the balance you have to strike between defence and attack in this league against opponents that have always got players that can hurt you."
On the Irons support, Potter says he can understand the general frustration.
"I completely understand where the supporters are coming from.
"I understand where the crowd are at because we haven't done well enough at home. We haven't won enough and played well enough, so you can understand there's a frustration there.
"This is normal and we accept that and we have to take that responsibility. But I think if they can see something, the crowd get behind us and then, like I said, it's a fantastic atmosphere and really pushes the team."