Saracens sit on minus seven points, 18 behind Leicester Tigers who are one of four clubs locked in the relegation scrap.
London Irish, who signed Waisake Naholo among others after being promoted this season, and Wasps, who have struggling playmaker Lima Sopoaga, Brad Shields, Malakai Fekitoa and Jeff Toomaga-Allen on their books, are other clubs dancing with dropping out of England's top tier.
Wasps blew a gift chance to improve their two-from-eight status after falling to the 35-31 defeat to Northampton.
Fekitoa, with a pick pocket try assist, and 36-year-old Jimmy Gopperth, preferred on the bench to Sopoaga, did their best to inspire Wasps but they could not maintain a three point lead with 10 minutes remaining, despite Northampton being reduced to 13 men after a red card to wing Tom Collins and yellow to South African halfback Cobus Reinach.
Taqele Naiyaravoro crashed over three minutes from time to seal Wasps' fate.
"To cough up an 18-point lead was very poor as we stopped trying to play and we were just defending," Boyd said. "I have no complaints about Tom's sending off but he was unlucky as I believe he was about to jump and get in the air but mistimed it and the contact came from their player.
"The yellow card for Cobus was also justified but I would question the consistency of the referee as, minutes later, their flanker did exactly the same thing and there was no punishment at all.
"At the end, we showed great resilience to poke ourselves and get in front, but we shouldn't have been in that position as we were pretty grumpy at half-time at not being further ahead."
Leicester appear to be improving after banking valuable points from their 31-18 defeat of Bristol, who copped two first half yellow cards to Alapati Leiua and Jordan Lay.
The loss dropped Pat Lam's Bristol Bears to fifth and they are now set for a spell without Charles Piutau after he damaged his MCL and suffered a broken nose in a nasty late collision.
"We worked our way back to 7-6 and then at half time I showed the boys the clips, we were shocked and unrecognisable in what we were doing," Lam said. "At half time I said it was a great challenge, we've been here before. We got it back to 21-18 and there was a couple of moments where we just didn't score.
"The sin bins were silly, they were unnecessary. At the end of the day we had enough chances to get ourselves back into the game that could've easily blown up if it weren't for some silly stuff from us."
Elsewhere, Jason Woodward bagged one of Gloucester's four tries and Willi Heinz stood out in their 29-15 victory over Bath. Sale Sharks also thumped Harlequins, running in six tries in their 48-10 win.
In the French Top 14, Toulon scored six tries in their 43-3 victory over Castres in a match that featured six cards. The win lifted Toulon to third, 11 points behind Bordeaux.
In other results, Jerome Kaino's Toulouse were stunned 30-18 by lowly Stade Francis. Ben Tameifuna celebrated his 100th match with a try as Racing defeated Clermont 27-19, and Victor Vito scored for La Rochelle as they toppled Pau 44-13.
In the Pro 14, Dave Rennie's Glasgow Warriors registered a 38-19 win over Benetton to remain third and Brad Mooar's Scarlets notched a 16-14 away victory over Cardiff as they improved to second in their pool.
Irish powerhouse Leinster, who thumped Connacht 54-7, are again the team to beat.
