Rangers striker Kenny Miller said his team was embarrassed by their 5-1 home loss to Celtic and said a lot of work was needed to build a side that could challenge for honours.

The veteran forward got on the scoresheet but it was no consolation as he admitted the day was one to forget.

"I think the lads feel, disappointed isn't a strong enough word.," he said."You're ashamed to play your part in a performance like that , embarrassed by the result."

The comprehensive defeat was the second in a week against their city rivals and underlined the gulf in class between Pedro Caixinha and Brendan Rodgers' respective squads. Miller said that the defending was poor and that there was a big task ahead to improve for next season.

"I wouldn't say it was like last week when it was levelled at us that we didn't lay a glove on them, didn't get close enough to them," he said. "I'm not saying that his week when the lads put a lot of effort into it but ultimately it wasn't good enough.

"When you look at the goals we lost again, they're poor goals. The decision-making leading in to the goals is all wrong so overall it's a really, really disappointing day, a really poor result and there's not really too many positives we can take from it.

"As I said before there's a lot of hard work has to go in to us in the close season. I'm bored of saying 'more competitive' and 'challenge' about next season.

"There's a lot of work and a lot of things we need to get right to put us in a better place and be more equipped next year."

Asked about the extent of change required in the playing squad, Miller was reluctant to say but pointed at the points gap between Rangers and Aberdeen, as well as Celtic, as evidence that the current squad wasn't achieving enough.

"That's not for me to say [about recruitment]," he said. "That's work that the club'll do, the manager will do and he's the one that will assess his squad and where he feels he needs to strengthen but you just need to look at the league table.

"We seem to get carried away because of where we are as a football club and where we've been in the past, being up there challenging and being successful and winning trophies and challenging Celtic.

"You need to look at the league table so see how much work has to be done and how much better we need to be next year."