The black, green and gold currently sit four points adrift of fourth-placed Exeter Chiefs, but with a game in hand.
And with just four matches of the regular season remaining, Saints, who go to Bath on Saturday, know they can't afford any more slip-ups as they seek to secure a play-off place.
"We've never won at Bath since I've been here and we need to win to stay alive in the race for the top four," Boyd said.
"We know if we lose, we're gone.
"If we go down there and say we were complacent then we certainly don't deserve to be there.
"I don't think complacency will be an issue.
"If we play well enough we'll win, if they play really well then maybe they'll win.
"It certainly won't be because of complacency."
Bath are currently bottom of the table, having won just four of their 20 league games this season.
But Saints have not won at The Rec since December 2015, so they know just how tough this fixture will be.
"They're a team full of good individuals and they've got some good youngsters there as well," Boyd said.
"They haven't had their best season but you would take them lightly at home at your peril.
"They're a tough opponent.
"We haven't had any luck down there in the four years I've been here - it's the only ground I haven't won at in the Premiership.
"History tells us it's a tough place for us to play.
"They've got a lot of good individuals there and it's a sleeping giant in a lot of ways.
"We respect the challenge that's coming on Saturday."
Saints go into the game on the back of a 31-21 Challenge Cup last 16 loss at Gloucester last time out.
That brought an end to a five-match winning streak for the black, green and gold.
"We've separated it out because it's in a different league and we're disappointed to surrender meekly in our European campaign," Boyd said.
"From a performance point of view, we weren't happy with that.
"We gave them a 21-0 lead and we didn't have enough to peg it back.
"It was our worst performance for the past couple of months.
"When the reward was big, we didn't deliver so that was poor.
"There's internal disappointment and expectation and the guys know their effort wasn't good enough.
"Credit to Gloucester because what they do they do well and they did other things better than we thought they would so we wish them well in their quest going forward.
"But our performance wasn't of the standard that we were expecting and we'll go back to our key drivers, key non-negotiables and reset that.
"We know we're in play-off football so if we get it wrong again we'll be preparing for next year.
"We've been playing knockout rugby in the Premiership for the past three or four weeks really.
"We didn't have any lives left a few weeks ago and we don't have any left now.
"If we don't get it right against Bath our season is pretty much done.
"The team's stood up to the challenge well of playing knockout football and if it doesn't this weekend then we'll pick through the bones of why and move on accordingly.
"We're certainly looking to continue this weekend."
Elimination from European competition means Saints will only play one game in May.
That will be a Premiership clash at Saracens as the other weekends in that month are reserved for Champions Cup and Challenge Cup matches.
And that leaves Saints searching for a solution to a lack of regular game time.
"We have one game in the month of May," Boyd said.
"We play two games now then we have two weekends off, then there's a Premiership game and then another weekend off for the European finals, then we play the final game in the league.
"I don't think anybody who is looking solely at the Premiership would say to have three weeks off in the last five weeks of the competition is an optimal way to run the Premiership.
"It's an age-old problem in the northern hemisphere in how you marry the international game with the domestic game is a really interesting conundrum and no one has come up with a good solution.
"I doubt anyone would say playing one game in May is a good thing for anybody.
"Even two weeks off in a row is probably not ideal.
"We're sitting down with our medical and coaching people and trying to decide what we do.
"Do we go to another club and try to play a friendly game? Do we have an internal game? Do we just do training? How much time do we give them off?
"When you've got two weeks off, one game, one week off, one game, it's tricky."