Dalot struck the opener - his first goal at Old Trafford - before that was pegged back Soungoutou Magassa.
Afterwards, Dalot reflected: "Disappointed. At 1-0 up with 30 minutes to go, I think we have to control the game much more. Especially at Old Trafford. We cannot get as anxious as we got after the goal. We were maybe a little bit more sloppy with the ball possession.
"Obviously disappointed with the draw. We had the game, there.
"It's the solution that we need to find. It can be various things. It shouldn't be like this because you are fighting 60 minutes to score a goal and then when it happens you should keep doing the same things, even more controlling, longer possession so we can be dominant. Especially the play that goes to the corner that we conceded - that's the kind of play that we need to avoid, especially against teams that are good on the counter.
"And we knew today that they were going to be looking for counter-attacks and set plays and unfortunately we couldn't hold the result but in the end we have to look to ourselves - I think it's more our fault, than credit to West Ham."
On his first Premier League goal at Old Trafford, Dalot also said: "It's a great feeling. Any time you have the opportunity to score for a club like this, it's amazing. Especially at the Stretford End. But in the end, the taste is not the same, I would change that for the three points without thinking. But I'm happy to help the team in any way, whether that's with a goal or whatever.
"But this type of result, it just gives you something to look at. We cannot be winning at home with 30 minutes to go and not controlling the game."
On dropping two points at home, he added: "I think it's massive. We're at the time of the year where you cannot drop too many points, otherwise the distance to the top will be even higher. This season, the distance is short, but it will come to a time when everyone starts spreading out and we want to be there, we want to be in the top four, top five. That's the aim, we have to be there.
"Today we had a big chance, I think that's why the disappointment is even bigger."