KENNY Miller remains convinced that Rangers supporters will continue to back the Ibrox club in large numbers this summer despite tens of thousands of them leaving the Celtic game at the weekend early in disgust.

However, the striker, who signed a one year contract extension with his boyhood heroes last Friday, has conceded his side will have to perform far better in future in order to ensure the continued loyalty of fans.

Pedro Caixinha’s side was thrashed 5-1 at home by Brendan Rodgers’s team in a one-sided Ladbrokes Premiership match on Saturday – a humiliating defeat that proved too much for many of their followers to bear.

An unprecedented number of them left the stadium during the course of the Glasgow derby game and the stands were half-empty when referee John Beaton blew the final whistle at the end of the 90 minutes.

A record 43,000 people bought season tickets last summer on the back of Rangers winning promotion to the top flight of Scottish football and bringing in high-profile signings like Joey Barton and Niko Kranjcar.

But the Govan club have, despite reaching the Betfred Cup and William Hill Scottish Cup semi-finals and being on course to clinch a Europa League qualifying spot, failed to live up to expectations in the 2016/17 campaign.

Miller, though, has no concerns about whether fans will carry on backing Rangers, who are still wrestling with historical off-field problems and operating at a loss, to the same extent as they have this term.

"That's the one thing that will never change,” he said. “The fans have been outstanding throughout what has been a tough, frustrating season for everyone at the club. We've not hit the levels we have been expecting to hit since day one with the draw against Hamilton at Ibrox.

“We've had no level of consistency or performances. We have had maybe two or three games in a row. But I think our best run has been four wins in a row. Listen, that's not good enough to be up there challenging for the top.

“We are still some way behind Aberdeen in second spot. So there's a lot of work to be done to be in a position for us to be better next year."

Miller continued: "We all know what's happened to the club over the past five years and it was always going to be hard. We were all hopeful we could get back straight away and challenge and everything would be great. But it's not gone according to plan.

“So, yes, it is frustrating at the fact we are where we are at the moment and are finding it tough. Whether it's a gulf in quality or the fact that the mental side of it is creeping in now, because we are going into games knowing we have had poor results against them this year, I don’t know. But, to be honest, I'm not looking at Celtic and saying we need to do this and that. We just need to get better."

Asked if he thought would be reflected in season ticket sales in the close season, Miller said: "I wouldn't think so because their support has been unwavering apart from a wee spell when there were other issues involved. But it's up to us as players and staff to get a team out that they can be proud of."

Miller, who scored a late consolation goal, admitted he had been “ashamed” and “embarrassed” to be involved in such a poor Rangers performance, but he stressed that he was determined to put it behind him by helping the third-placed Premiership team record a win over Partick Thistle at Firhill this Sunday.

The 37-year-old is confident that Caixinha can help to revive the fortunes of the Rangers squad by signing some quality players during the summer.

"This is not the first 5-1 or 6-2 or 7-1 or whatever the results have been in the past,” he said. “It's about how we react, how the club reacts with the business we will do in the summer. The summer is going to be crucial to us.

“At the moment, it's about how we react when we play Partick next week. Are we going to whittle the season away, let it run down, maybe win a game and draw a couple? Or are we going to get back and get a positive reaction from this and win our last four games. For me it's the latter.

"I'm part of the squad and I am ashamed and embarrassed to be part of a performance like that,” he said. “It's the second 5-1 of the season, home and away. We were all working hard because we know the work that has to be put in for us to be better next season."

Mark Warburton parted company with Rangers in controversial circumstances after a disappointing run of results back in February and under-23 coach Graeme Murty took over on a temporary basis until Caixinha was appointed.

But Miller has refused to blame off-field upheaval for the failure of the team to live up to expectations this season.

"I'm a footballer,” he said. “I just go and train every day as hard as I can and try and go and win games of football. Other things are off-field stuff. Clubs deal with things like this all the time. So they are no excuses. As a team and as a club we have underperformed this year. To be a successful team in any league, you need to have a high level of consistency and we've not done that."