The Gers were comfortably beaten 2-1 by arch-rivals Celtic in the Hampden showpiece while Kilmarnock drew 1-1 at home to Motherwell the day before.
Match preview
Michael Beale suffered his first defeat as Rangers boss in the League Cup final last weekend after winning 13 of his opening 14 in the dugout.
Celtic's Kyogo Furuhashi found the net on either side of half time before Alfredo Morelos bundled one in for the Gers who somehow avoided conceding again in the final 25 minutes despite affording the Bhoys numerous chances.
Beale claimed to be "super-optimistic" about his future but criticism has been quick to gather in the wake of a controversial team selection for an underwhelming outing in the final - although, whatever XI the manager picked would be under scrutiny if his side lost.
Rangers have not been beaten by Scottish opposition at Ibrox since April when Celtic - them again - earned a 2-1 win while the Gers were focusing on reaching the Europa League final.
Derek McInnes was not underselling the dire state of his side's away form when he described it as "horrendous", with Killie collecting a pitiful two points from 42 available on the road this season.
Killie are the division's lowest scorers at any ground this term but have mustered just five league goals away from home all season - Rangers' right-back James Tavernier has scored six away goals on his own throughout the current campaign.
Scott Robinson scrambled a scrappy opener over the line against Motherwell last weekend but Killie were undone at the death as Callum Slattery spanked a stunning free kick into the top corner to snatch a draw in stoppage time.
Any points dropped by Killie on home soil - or rather, Rugby Park's artificial turf - are crucial given their away woes, with last weekend's draw leaving McInnes's side second-bottom, four points above Dundee United.
The Ayrshire outfit have not beaten Rangers at Ibrox since Kris Boyd - the former Gers striker - scored the only goal of a Premiership game in 2018 for a Kille side managed by the current Scotland national team boss Steve Clark.
Rangers Scottish Premiership form:
W
W
W
W
W
W
Rangers form (all competitions):
W
W
W
W
W
L
Kilmarnock Scottish Premiership form:
L
L
W
L
L
D
Kilmarnock form (all competitions):
L
W
L
W
L
D
Team News
Both John Lundstram and Malik Tillman started against Celtic despite coming into the contest after fitness struggles - Beale may be tempted to give this duo a rest after their Hampden excursions.
Tom Lawrence and Steven Davis remain sidelined with knee injuries while Ridvan Yilmaz is nursing a hamstring problem.
John Souttar (ankle) and Filip Helander (foot) could be back at some point this month but are unlikely to be available as soon as Saturday.
Kyle Vassell is set to serve the second game of his suspension on Saturday after receiving a straight red card in Kilmarnock's limp loss away to Hibernian a fortnight ago.
Centre-back Lewis Mayo has featured in every league game except those against his parent club, Rangers, with that clause in his loan agreement sidelining him again this weekend.
Doubts linger over Liam Donnelly after he sustained a knock while Jeriel Dorsett returned to training in the week leading up to the trip to Ibrox.
Ben Chrisene has been hampered with a knee injury since January while Innes Cameron is expected to join him in the treatment room for an extended period with a hamstring problem.
Rangers possible starting lineup:
McGregor; Tavernier, Goldson, Davies, Barisic; Raskin, Kamara; Sakala, Cantwell, Kent; Morelos
Kilmarnock possible starting lineup:
Walker; Alebiosu, Wright, Taylor, Stokes; Armstrong, Polworth, Power, Chambers; Doidge, Robinson