A late equaliser from Jake O'Brien canceled out Tomas Soucek's opener for West Ham.
After facing his former club, Moyes later told evertontv: “(The players) didn’t give in and it’s great that we’ve got real spirit in the dressing room.
“They dig each other out, they’re after each other if we’re not playing well. We weren’t happy at half-time. We could have played much better. The penalty kick looked as if it didn't go for us just on half-time.
“We hadn't done enough that wrong in the first half. We just hadn't done good enough to probably get the goals.
“And I think Graham Potter has been talking a lot about how they're trying to stop conceding goals. They were much stronger, much harder to play against today – not much room to run behind them."
On Charly Alcaraz's performance, Moyes added: “Well, we thought it might suit because of the way that West Ham might possibly line up. We didn't want to get outnumbered in midfield.
“We're playing him a little bit out of position but at the moment. (Abdoulaye Doucoure's) form has been very good. Charly's scored goals, came on and made the difference, so I wanted to see if I could find a way where I thought it worked for both of them.
“I think in some ways it did, but in other ways, it didn't really get the best out of Charly in his position. I thought, as well, that we didn't have much space to run in behind in the first half.
“So that affected us a little bit in how we set up, but we made a couple of changes and that freshened things up a little bit. But we're having a look, we're having to see how we can be adaptable.”