Boss Graeme Murty apologised to retreating Rangers fans after their side slumped to a 4-0 William Hill Scottish Cup semi-final defeat to Celtic.
Goals from Tom Rogic and Callum McGregor gave the Hoops a comfortable and commanding interval lead at Hampden.
Gers defender Ross McCrorie was given a straight red card by referee Bobby Madden just after the break for denying Moussa Dembele an obvious goalscoring opportunity and the French striker scored from the spot. As did midfielder Olivier Ntcham in the 78th minute, by which time thousands of Gers fans had left the ground.
Read more: 'It's not about me': Graeme Murty avoids talk of Rangers future after Celtic defeat
A distraught-looking Murty admitted it was "definitely" the lowest point of his admittedly short managerial career but refused to answer a question about whether his players had let him down.
However, asked if he had a message for the supporters, the former Gers under-20s boss, said: "I would apologise to them for the game. I would ask for their patience and to keep believing but it is no good to keep asking it.
"You have to go and put a performance in to be worthy of their support.
"I thought our support was fantastic. It has been brilliant the whole time I have been here, it has been absolutely outstanding.
"We didn't do enough to make them want to stay at the stadium today."
Murty was put in charge in December for the rest of the campaign but his chances of keeping the job next season look to have gone.
Asked about his appetite for staying on, he said: "I am not going to talk about my role, I think it would be churlish and selfish in the extreme to talk about my own situation in the rawness of that."
Murty added: "It is a lonely place standing on the sideline when that is going on. But I don't think words is enough to convey how I am feeling right now.
Read more: 'It's not about me': Graeme Murty avoids talk of Rangers future after Celtic defeat
"There is a lot of things we can look at. In the raw emotion right now, I didn't think we got close enough to them, allowed them to play too easily.
"But all four goals were easily avoidable though basic, good defending and in the second half we gave them a penalty and sending-off which made their job far easier."
Celtic's seventh successive title win is inevitable - they need only one win from five post-split fixtures - and they are within 90 minutes of an historic second successive treble when they play Motherwell in the final.
However, Rodgers - who has gone 10 Old Firm games unbeaten since he arrived in Glasgow in 2016 - insists he is only looking towards the trip to Easter Road to play Hibernian next week.
He said: "The mantra is the next game.
"We are in the final now and that won't be an easy game either, that is a totally different game again with their physicality.
"They are a very honest team, they work very hard but we know that when we turn up and play, it gives us a great chance.
"But we have a job to do now. We have to finish off the league campaign. We are in a really good position there.
"We have five tough games to finish but we want to finish the season well and be back here in good confidence and look forward to that. "
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