"It was a very tough game, which we knew it was going to be," he says, "and we were probably fortunate to come away with a point - although we had chances, having hit the post and created other opportunities.
"They played very well and you have to give them a lot of credit. They are a good side who are going to create chances from midfield.
"Fair play to them - they probably felt they should have had more than a point and it would be hard to disagree.
"It would have been nice to score the winner but at 1-0 I don't think you are ever safe, particularly against a side like Millwall, who seem to be playing very well at the moment.
"It was the first of these derbies for 10 years and it was never going to be a game against a team that you are just going to walk over.
"If people just think that they are mistaken because none of the games in this league are easy and Wednesday will be another tough one.
"It was nice to get on the scoresheet against Millwall. I felt I had maybe earned one against Cardiff but it didn't quite come; I got one on Sunday but it was just a shame we couldn't hold on to the three points."
West Ham are now a win away from the top having lost ground recently and David says: "We are three points off the top but that three point gap is vital compared to just one if we had won.
"But it is a tough league and every game is hard. If you don't scrap and fight and play good football, pass it around and show for the ball as well, we are not going to pick up the three points - and that is what we have to start to do."
David, who has just begun studying for a university degree, misses the Norwich game through suspension for earning a fifth yellow card of the season.
That is something Trevor Brooking desperately wanted to avoid David picking up in the next two games, as it means he will be missing for one of the two games that Jermain Defoe has to sit out following his sending off at Gillingham.
And it removes the delight at David's yellow card at Crewe being scrubbed off after the referee decided that his collision with goalkeeper Clayton Ince was accidental.
"That is disappointing. There were a few silly bookings this season but it was going to come as I was on four - let's just get that out of the way rather than be teetering on the edge.
"I will miss a game that Jermain misses as well, and that is a shame, but in an atmosphere like Sunday sometimes these things happen.
"The referee said the linesman spotted it and called him over but there you go."
David is warning against complacency in the first division, and he should know after two successful seasons in it for Wimbledon.
But the player who once scored 42 goals in 48 games for Excelsior in Holland - and picked up a Dutch Player of the Year award as a result - is desperate to prove himself in the Premiership as soon as possible and does not want attitude to adversely affect West Ham's chances of getting there.
"There is a lot to play for and these games are hard - they are not going to be a walkover and everyone now realises that," he says.