RANGERS captain Kenny Miller admitted he was “disappointed, ashamed and embarrassed” by a second 5-1 derby defeat of the season but felt the Ibrox side now needed to follow the Celtic blueprint if they are to post a stronger challenge next season.

The performance of Miller, who signed a new one-year contract extension on Friday night, was Rangers’ sole bright spot in an otherwise abject team performance and he also scored their consolation goal with Celtic four ahead. Manager Pedro Caixinha later insisted he would shoulder all the blame for the loss but an angry Miller said the players needed to carry some of the share of the burden.

“Disappointed isn't a strong enough word,” said the striker. “The boys feel ashamed to play a part in a performance like that. We're embarrassed by the result. A lot was levelled against us last week [after the Scottish Cup semi-final defeat] about not getting close to them, not laying a glove on them.

“I wouldn't say that here but ultimately it wasn't good enough. The goals we lost were poor, as were the decisions which led to them. It was all wrong. Overall, it's a really disappointing day and a poor result for us. There aren't many positives we can take from it.

“There's a lot of hard work will need to go in from us over the close season. But I'm bored talking about us being more competitive or putting up a challenge. It's just words. Next season, a lot of things need to be put right – to put us in a better place to be more equipped. It's not for me to say how many changes need to be made. That's up to the club and the manager.”

Celtic have been a side transformed this season since Brendan Rodgers succeeded Ronny Deila as manager, the Northern Irishman bringing in a higher calibre of player. Miller feels Rangers will need to do something similar in the summer if they are to get closer to their rivals next season.

“The gap is big in terms of points,” he added. “But you only have to look at Celtic and what a difference a few players can make. There's no doubt that we need to strengthen and we need to be better.

“It's not about signing a whole new team. There's no proof to say that will be an answer. But Celtic are the prime example of the difference a few better quality players can make. And a few of the ones already there being. Just look at Celtic – a few players of a higher quality can make an incredible difference to a team. But that’s up to the manager to sort out for us next year.”

Leigh Griffiths wasn’t involved when Celtic beat Rangers by the same scoreline earlier in the season, and was an unused substitute when the champions won at Ibrox on Hogmanay. His celebrations at the end – having scored Celtic’s second goal – were understandable.

“It felt amazing,” he said. “I have come here and scored. There was the one on New Year’s Eve but unfortunately I didn’t get on the pitch. To be a part of this one then was massive for me. I have had injury problems this season but I am fully fit now and it is my chance to step up and score goals between now and the end of the season.

“But it’s not just about my performance or my goal, it’s about the whole team’s performance, the way we played. We were very professional in the way we went about it.”