Defender Miguel Britos was sent off for head-butting an opponent as Napoli lost 3-1 at champions Juventus on Saturday, all but ending their hopes of Champions League football next season.
Roberto Mancini's Inter Milan will finish outside the Europa League places after they lost a thriller 3-2 at Genoa.
Napoli can now only qualify for the Champions League if Lazio lose to AS Roma in their derby on Monday and Napoli beat Lazio in their final game.
Their defeat also meant that second-placed Roma qualify at least for the Champions League preliminary rounds.
With Napoli trailing 2-1 in stoppage time, Britos lost his temper and head-butted Juventus striker Alvaro Morata.
The Uruguayan was shown a straight red card and conceded a penalty, which was converted by substitute Simone Pepe.
Champions League finalists Juventus rested several regular players, but still went ahead in the 13th minute when Kingsley Coman dinked the ball over the defence and Roberto Pereyra fired past Mariano Andujar.
Napoli coach Rafael Benitez took off misfiring forward Gonzalo Higuain at halftime and his side equalised five minutes after the re-start.
Napoli were awarded a penalty for handball and, although Lorenzo Insigne had his effort saved by Gianluigi Buffon, David Lopez fired home the equaliser.
Buffon made two decisive saves, tipping a long-range Lopez shot over the bar and blocking Marek Hamsik's header.
Stefano Sturaro gave Juve the lead in the 77th minute, turning past his marker and placing the ball beyond Andujar for his first goal for the club.
Napoli were left with 63 points in fourth place while Roma, in second, have 67 and Lazio 66. The team finishing second go straight into the Champions League group stage and third place earns a place in the final qualifying round.
Inter's defeat left them eighth with 52 points and ended their hopes of the top-six finish they needed to qualify for the Europa League.
They could still sneak in, however, if they finish seventh and Genoa (59 points) lose their appeal against a ruling which has denied them a licence for European football.
However, Inter would still have to make up a two-point gap on Sampdoria (54 points) who have a game in hand.
Mauro Icardi put Inter ahead, Leonardo Pavoletti equalised and Rodrigo Palacio restored the lead for Inter on the half hour.
Genoa levelled again before halftime and Inter were agonisingly close to a winner in the 74th minute when Hernanes' low drive bounced off the post and Marcelo Brozovic fired the rebound against the crossbar.
Junaj Kucka then headed an 89th-minute winner for Genoa.