Dagenham and Redbridge manager Wayne Burnett praised his players following their 1-0 victory at League 2 basement side Torquay United.
Medy Elito latched on to an Adebayo Azeez flick-on before being felled by Torquay right back Dale Tonge to win a 67th-minute penalty, which he took himself and scored.
The defeat leaves Torquay eight points adrift of safety with three games remaining and a Devon derby trip to Exeter on Monday in the offing.
Burnett said: "The players knew they didn't play well last week and they gave a real response today and I am proud of every one of them.
"We have to keep going right to the very end, I said to the players that we have to respect the other teams who are either fighting for promotion or fighting off relegation."
The nearest United came to replying was in the 82nd minute when Krystian Pearce's audacious flick from substitute Jordan Chapell's corner from the right was cleared off the goal-line by Daggers defender Femi Ilesanmi.
Torquay defender Pearce was twice denied by visiting keeper Chris Lewington in the sixth minute following a Courtney Cameron free-kick from the left. Both times Pearce was quickest to react but his efforts were blocked on each occasion by Lewington.
Post-match disappointed rookie Torquay manager Chris Hargreaves declined to talk to the press.
Dagenham boss Burnett added: "I thought it was quite an even game. They looked most likely to score from a set piece. They had one or two chances but our goalkeeper wasn't really troubled that much.
"You come away, and are playing a side are fighting for their lives, no game is easy now and Torquay kept going and going.
"They changed it to 3-4-3 and we got a little bit of space but when we started passing it we did okay.
"We didn't pass it enough and sometimes they are too eager, too keen to try and put the ball straight into the goal instead of keeping it and passing it. It will open up naturally.
"But it's been a long season and I can't fault my players because they have worked incredibly hard and some of them actually looked quite tired today.
"Medy is sharp around the box and you give him a yard that's what you get. I thought it was a penalty, he's despatched it and it's given us the victory.
"Near the end they were chasing the game and left holes and left pockets - and I would have done exactly the same - and we have got a lot of pace in our team so we were always capable of hitting them on the counter."