The Irons remain rooted the foot of the table as they continue to search for a first Premier League win since September 25.
Peter Odemwingie had put the Baggies in front from the penalty spot on 28 minutes, but West Ham fought back level before the break when Scott Parker smashed in a 25-yard effort.
Indeed, Frederic Piquionne sent the Irons ahead from the spot at the start of the second half and then missed a great chance to make it 3-1 before Pablo Ibanez headed in an equaliser to earn the visitors a share of the spoils.
Avram Grant, however, continues to remain positive, despite his side's predicament, citing signs of improvement in recent performances, if not results, having thrown away a two-goal lead at Birmingham on Saturday.
"The reaction after they scored was good to get to 2-1 and then we had a great chance to make it 3-1 and dominated the game," Grant said.
"I thought we were going to win, but we conceded a goal and it is disappointing."
Co-owner David Sullivan had claimed West Ham needed to collect "at least seven points" from the run of games against Birmingham, West Brom, Blackpool at Upton Park on Saturday and then away at Liverpool - or "we know we have a real problem and that we have to shuffle the pack".
Under-fire Grant, however, insists no-one craves victory more than the team.
"We want to take points not because anybody else wants them, but because we want them and we deserved to take them," said the former Chelsea and Portsmouth boss, appointed in the summer.
"We are very close to it - when the first win comes, we will win more and we are playing football to win games.
"We have had a lot of injuries and it is not easy.
"We keep our style of football, it is not going like we want, but we are playing well and that is what frustrates us more than anything.
"The fans understand, they want more points, but no one more than myself and the players and staff want them.
"Everybody can see we play good games of football, from my experience if we continue like this, then the points will come."
Grant continued: "In the past, we have not reacted very well, now we react very well and continue playing.
"We are not a team who can go back and defend with eight or nine, we continue to play.
"But we will of course analyse the game and see what we can do better.
"The way we have conceded goals is something we need to think about."
Grant was less than impressed by the penalty award against his team, when Luis Boa Morte wrestled Steven Reid to the ground at a corner.
"I prefer not to speak about decisions," he said.
Baggies boss Di Matteo, meanwhile, was happy enough to have left London with a share of the spoils.
"We controlled the game quite well, although we gave them an early Christmas present just before half-time which put them back into the game," di Matteo said.
"The second half almost turned in their favour, but we managed to get a deserved equaliser and were a bit disappointed as we thought we could have got more out of the game, but we would take a point away from home."
On the performance of Mike Dean, who gave West Ham a spot-kick when Gabriel Tamas bundled over Kieron Dyer, the Baggies boss said: "The referee had a good game, and handled the pressure well.
"I thought he got the key decisions right, although it was difficult to see.
"Our penalty was obvious and he was in a good position when he gave West Ham a penalty."
The Baggies have impressed on their return to the top flight, but Di Matteo warned the hard work must continue: "It was very important for us not to have three defeats in a row, and to get a good performance.
"People outside the club may get carried away, but we are new in the Premier League.
"We are still trying to learn and need to manage games better, need to get that lead into half-time.
"But we are improving game by game and will get better."