Caretaker boss Dave Woozley insists Crawley cannot afford to relax in their battle to beat the Conference drop.
Reds edged to the brink of securing safety with a crucial away victory against relegation rivals Stafford Rangers.
It takes them six points clear of the danger zone going into today's home clash against play-off contenders Exeter City and beyond the 50-point mark, regarded as the magic number needed to stay up.
One more win from the remaining five games would probably be enough and, having been unbeaten in their last five games, they should have no problems achieving it.
But Woozley has warned against falling into the complacency trap.
He said: "We are not looking at just getting one more win because you don't know what might happen.
"Before the Stafford game we set ourselves a target of 12 points from the six remaining games and that was not us being optimistic.
"It was genuinely what we thought was achievable and what the squad of this ability is capable of.
"So there is no way we are going to sit back and just get the points needed to stay up. We want to keep our run going and get as high up the table as possible."
On the day Dagenham secured promotion to the Football League, Reds took another significant step towards survival after producing a classic snatch-and-grab away win.
They scored a scrappy early goal with their first shot after seven minutes and spent the rest of the game defending it desperately.
It was one of the few occasions this season Reds had ditched their football principles in favour of a more defensive approach.
Woozley, who led the resistance at the back, made no apologies for the display and says Crawley would have been naïve to play any other way.
He said: "The pitch dictated the style of the game. It was hard, bobbly and dusty and I think the lads would have been better off wearing trainers.
"We had to play in a different style because we knew it was going to be a scrap, with them fighting for survival as well, and the lads once again stood up to be counted.
"We couldn't play any other way. We couldn't get the ball down and pass it around on a pitch like that because it would have led to basic mistakes and we would have got caught out.
"We had to adapt and we stuck to our task well. Once we got the ball we didn't just go negative, we tried to attack but the priority was not to lose."
The goal that settled it summed up the game as a whole. Midfielder Steve Evans picked the ball up 20-yards from goal after a hashed clearance by defender Nathan Talbott and saw his shot take a big deflection off Richie Sutton and spin into the opposite corner.
Evans had been brought back into the side following injury to replace the suspended Tony Scully.
Woozley said: "It was probably a blessing in disguise that Tony was missing. Evo came in and not only scored the goal but was able to win the second ball and scrap because he is more of a defensive player.
"That is exactly what we needed because it was never going to be a game for the likes of Tony Scully."
Reds sat back and soaked up the pressure after the strike and tried to hit Stafford on the break.
It handed the impetus to the home side but they found Crawley's defensive barrier hard to break down and eventually ran out of ideas.
Cameroon striker Guy Madjo was the only player who looked capable of unlocking the door.
He went closest just after half time when Ben Hamer made two brave smothering saves at his feet after he was left unmarked at the far post from a Robin Gibson cross.
The impressive Hamer had to be at his best again soon after when he produced a point-blank parry from Craig Lovatt's drive following more good work by Madjo.
And veteran forward Neil Grayson completed a hat-trick of near misses for Rangers when he dipped a volley from the edge of the box inches over.
Woozley is expecting a completely different game against the Grecians today.
He said: "Exeter will come and play and hopefully that will bring out our strengths as well.
"We will be able to use the midfield a bit more and be more of an attacking threat. We have only got two home games left so we want to put on a good performance for the fans."
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