Ian Baraclough believes Motherwell still need to keep "one eye" on avoiding automatic relegation despite being seven points clear of bottom team St Mirren.
Lee Erwin's winner in a 2-1 victory at Kilmarnock created much needed distance between 'Well and the Buddies.
"We've got to concentrate on winning games of football until it's mathematically impossible to be relegated outright," Baraclough told BBC Scotland.
"We'll try and drag teams above us into it."
With seven games to go, 11th-place Motherwell are three points behind Ross County in 10th, with the Dingwall side winning 2-1 at Dundee United.
The Steelmen, for whom Stephen Pearson cancelled out David Syme's opener at Rugby Park, have now won three of their last five matches.
"We've come away with three points and it's what we came searching for," said Baraclough, who was appointed boss in December.
"We had to dig deep for it as it certainly didn't go our way the first half an hour. We suddenly realised we had to go and battle and do the horrible things.
"We came out and bossed the second half; left them to one or two scraps and defended very well."
Pearson, capped 10 times for Scotland, signed a two-year deal on Friday after initially rejoining the Fir Park side until the end of the season.
"It's been a massive couple of days for him," said Baraclough.
"I've been on at him; I think he can score more goals. The amount of runs he makes breaking into the box; he should be getting more efforts on goal.
"It's fallen for him today and he has put it away, so really pleased for him."
The former Sligo Rovers manager was equally pleased with 21-year-old Erwin, who scored his second goal of the season - his first being back on the opening day of the campaign.
"He can be what he wants to be," he added. "Since I've come in who can really affect defenders; can show good power and explosion behind back fours.
"All he needed was a goal. His performance today warranted a goal."
Kilmarnock manager Gary Locke was in charge of the club officially for the first time and felt his side had deserved a penalty when the score was 1-0 in their favour.
Chris Johnston had made a fine run into the box and it was difficult to tell whether a foul, or simply momentum, had grounded him.
"I felt he'd been touched," Locke told BBC Scotland.
"He's a young lad and he's obviously tried to stay on his feet - maybe in the future he'd be better going down.
"But a lot of positives first half. David Syme was playing against a really good player in Scott McDonald but I thought he acquitted himself well.
"Good to see him get the goal but he's a defender so I'd rather see us keeping clean sheets."