Rangers succumbed to a record-extending fifth consecutive home defeat as Hibernian won 2-0 at Ibrox to extend their unbeaten league run to 16 games.
Celtic can now seal the Scottish Premiership title before their Glasgow rivals play in the league again with victories over St. Johnstone on Sunday and Kilmarnock next weekend.
"Angry, really angry in fact - that's the most simple way I can put it. There's no way I'm accepting that," said Rangers interim boss Barry Ferguson.
"I'm not going to kid anybody on. Hibs deserved it. They tackled harder, ran harder and wanted it more."
Athletic Bilbao visit Ibrox on Thursday in the Europa League quarter-finals, but Rangers' poor domestic form has contrasted sharply with their exploits in Europe this season.
"It's about pride," Ferguson said.
"I know we're in the Europa League, but those are easy games to get up for."
Dylan Levitt opened the scoring in the eighth minute with a drive which went all too easily through Gers goalkeeper Jack Butland.
Martin Boyle raced away in the 69th minute to score a second to secure a first Hibs win in Govan in seven years and keep David Gray's men in third.
"We believe in the manager and the squad and the fans are fully behind us. The whole club is buzzing," said Boyle.
"We want to tie down that third spot."
Ferguson has enjoyed famous away wins at Celtic and Fenerbahce in the Europa League, but is yet to win in three home games since Philippe Clement was sacked in February.
Celtic's lead at the top of the table remains 13 points with a fourth consecutive title just a matter of time.
Aberdeen kept up the pressure on Hibs in the battle for European places.
The Dons maintained their upturn in form with a 1-0 win at Ross County to remain just one point behind Hibs thanks to Shayden Morris' winner.
St. Mirren's hopes of a top-six finish are fading after a 2-0 defeat at Dundee, who are just one point behind Kilmarnock and Ross County in the fight to avoid the relegation play-off.
Kilmarnock boosted their survival chances with a 2-0 win over Motherwell.