Jordan Archer and Matty Waters had put the Blues 2-1 ahead at the Chigwell Construction Stadium but the Daggers fought back and two late goals condemned Chester to defeat.
Bignot’s side failed to capitalise on their other relegation rivals being out of action but the boss saw plenty of things they can take forward.
Time is starting to run out for the Blues, however, and they now face a tough run of games against Bromley, Dover, Wrexham, Aldershot and Sutton.
Bignot told the Chester Chronicle: “It’s important we pick them up because there were a lot of positives today, which far outweigh the negatives, but obviously the scoreline is the biggest one, and it was a massive disappointment for us.
“It was a game we should have saw out. They got their fortune with the second goal. It was a contentious decision but from that point on we shouldn't have lost the game.
“I was really proud of the players' performance. They've given everything. Those last few minutes, they will learn from that, but unfortunately, they are learning in a difficult situation with the position we are in.
“I think you can tell by the performances that it's not a team lacking confidence. We've gone about our business, been positive, and we've gone so close to a result.”
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.