Steve Thompson says Latics need strength in depth to help them turn draws into wins.
For the third game in a row Oldham took the lead, this time through James Norwood in the fourth minute, but Dagenham pegged them back and equalised in the second half through Josh Rees.
Norwood and substitute Mike Fondop both had late efforts saved on the line in a finale that could have gone either way.
But despite stretching his unbeaten start as caretaker boss to six games, Thompson was frustrated that Latics not only failed to capitalise on their early dominance but again allowed the opposition back in.
And he feels key additions to the squad could be crucial in making them top seven contenders.
"They're giving us everything, you can't knock that, it's just that mentality that when we are playing well, don't stop doing it," said former Blackpool and Leeds assistant boss Thompson, who came to the club last season as head of recruitment.
"We seem to start doing bizarre things on the ball, we stop playing from our shape, we don't win our second balls, and I don't think it's a fitness thing, I think it's a mental thing because in the last 10 minutes we started to get a bit of tempo about us again.
"I've told the lads, we try to take all the excuses away from you, when you go out there you'll live by your decisions. We shouldn't be making changes, different shapes, to try to stop them playing. That's the frustrating thing for me.
"Me and Redders know what we need to take this team forward. I still think we need three or four players who can handle the ball, who have got legs. It's crying out for it. But on the flip side these lads give us everything, we're still unbeaten, but to go forward we know what we need."
Thompson added: "I think we need legs and people who can handle the ball, brave enough to get on the ball. They show us in training and show us in glimpses in the games what they can do, but it's not consistent enough. You can't pick a team not knowing what you're going to get.
"They're a great bunch, they give you everything, but to take it forward we need three or four more quality players in the team to help them and to bring them on as well."
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