Andrew Oluwabori scored the only goal of the game for the visitors, early in the second half at the Chigwell Construction Stadium on Saturday.
And Strevens was frustrated to end the afternoon empty handed, in front of a large 2,720 crowd celebrating Daggers Diversity Day.
“I’m gutted,” Strevens told the club website.
“We had a massive crowd in with great support for the boys and we managed to lose a game of football where for long periods we did some good things.”
Strevens felt the start of the second half was a key moment in the match.
“Being honest I thought we started the second half really passively and it was their best spell of the game,” said Strevens.
“It culminated in them getting the moment they did and it was a bit of quality from their lad on the edge of the box.
“They started the second half better than us and we didn’t get going.
“When we did, we were already 1-0 down.”
Dagenham came close to equalising in the 80th minute when Tom Eastman sent a header against the inside of the left post.
But the home side were unable to conjure up an equaliser after failing to make the most of the opportunities coming their way.
“We had good moments for the boys to score and we didn’t take them,” added Strevens.
“That’s partly down to good goalkeeping and good organisation from Halifax, but flipping it onto us we need to be more clinical with those chances because we created quite a few.”
Defeat left Dagenham sitting 14th in the table, just four points above the drop zone in a congested division.
But Strevens is now eager to bounce back at home to play-off pushing Altrincham on Saturday.
“I want to do better,” said Strevens.
“I need to do better as a management team and myself to make the boys better.
“I’ve got players in there hurting so I know they care.
“They’re fighting and trying to do the right things.
“It just seems like every time we have a good moment we take a step backwards.
“We need to go back forward again now and that’s what we have to do.”
And Strevens is also hoping Dagenham will benefit from not having a midweek match.
“It’s the first time we’ve had a free week in a while, so we have a few days to prepare,” said Strevens.
“This defeat is one that is going to sting but all of us will review it.
“We’ll look at the start of the second and we have to look at it collectively.”