Fallen giants Rangers were knocked out of the Scottish League Cup after Inverness Caledonian Thistle dished out a comprehensive 3-0 defeat in their quarter-final tie at Ibrox on Wednesday. Rangers had made a mockery of their Third Division status with a dominant display in a 2-0 win against Motherwell in the previous round and hopes were high around Ibrox that the Glasgow giants could claim another Scottish Premier League scalp. However, it proved to be a step too far for Ally McCoist\'s side as Inverness progressed to the semi-finals of the League Cup for the first time in their history thanks to goals from Andrew Shinnie, Gary Warren and a Graeme Shinnie penalty. McCoist said individual errors had cost his side dearly. \"I didn\'t think there was an awful lot between the teams in the first half. Neither team really created a lot but had reasonable amounts of possession,\" he said. \"They got the break with the goal but that said I thought the individual errors that cost us the three goals were extremely disappointing. In the second-half Inverness were better than us without doubt and deserved to be in the semi-final more than we do.\" His Inverness counterpart Terry Butcher was thrilled with his side\'s performance. \"I thought that they handled the occasion well and played some lovely stuff. \"Going 1-0 up we still had to weather a bit of a Rangers storm and we defended that well. The shape of the team was excellent and everyone worked hard. The players were really fired up for this and there is a lot of spirit in the team.\" Visitors take early lead Rangers had been desperate to give their fans a lift on the day the old club was liquidated at the Court of Session and an early error from Josh Meekings presented Dean Shiels with a chance but he flashed his shot wide. Rangers should have done better when Shiels sent Andrew Little clear in the box but the Inverness keeper blocked his shot with his legs. However, it was Inverness who took the lead in the 27th minute when Aaron Doran won a challenge with Ross Perry and stabbed the ball through for Andrew Shinnie who calmly slotted past Alexander. They doubled their advantage in the 59th minute when the Rangers defence were posted missing and Warren stooped to head Graeme Shinnie\'s in-swinging corner into the bottom left-hand corner. McKay was twice denied by Alexander when clean through before Inverness were awarded a 78th minute penalty when sub Anestis Argyriou upended Andrew Shinnie in the box. His brother Graeme sent Alexander the wrong way to bury his spot-kick low in the bottom left-hand corner to make it 3-0 and extend Inverness\' unbeaten run to eight matches. Hearts will join Inverness, Celtic and St Mirren in the semi-final draw after they claimed a 5-4 penalty shoot-out win against Dundee United after the match at Tannadice had finished 1-1 following extra time. Hearts had taken a 21st minute lead when Calum Paterson prodded home from close range after getting on the end of a low driven cross from Ryan Stevenson. United found themselves on level terms in the 35th minute when a shot on the turn from Michael Gardyne was blocked by Andy Webster and fell kindly for Johnny Russell who fired in from 14 yards. Hearts finished the match with ten men after Darren Barr saw red for his second bookable offence as the game headed to extra time. United came close to a late winner when John Rankin\'s 30-yard shot cannoned off the post in the final minute of extra time. Hearts recovered from missing their first two penalties to claim victory as Sean Dillion missed his decisive kick for United. From FIFA