The Hoops won 3-1 at Rugby Park to progress to the Co-operative Insurance Cup semi-finals.

The Japan international suffered some heavy tackles after Scott McDonald headed Celtic into a 15th-minute lead in the quarter-final tie.

He was booked by referee Craig Thomson for complaining about the treatment he was receiving before curling a free-kick past Alan Combe in the dying seconds of the first half.

Nakamura picked up an injury which saw him substituted at the interval but although Danny Invincibile pulled a goal back in the 67th minute, Aiden McGeady quickly restored Celtic's two-goal lead to take them into the last four alongside Rangers, Falkirk and Dundee United.

Strachan, with tongue in cheek, said: "There was a good chance of him being injured and he was hobbling.

"He was very brave and it's crazy in this day and age that Naka is the one that gets booked.

"He reacted by saying he got tackled and he pointed four times. The referee obviously booked him because it was only three. If he is going to complain about tackles then he has to get it right!

"I told the players not to lose their focus and to get on with it and win the game.

"What Naka did was put the ball down and put it in the back of the net. That's the best way of answering anybody who wants to take you out of the game.

"I was happy to get through."

Celtic defender Gary Caldwell, skipper on the night in the absence of Stephen McManus, revealed he wants to finish his career at Parkhead.

Celtic have triggered a one-year extension in the Scotland defender's current deal and are in talks with Caldwell's representatives about a new contract.

The former Hibernian player said: "It's a great club and I've enjoyed every minute that I've been here.

"When you come to Celtic you realise what a big club they are and appreciate every game you get and every time you go out on the park.

"It's a club you would love to stay with your whole career and hopefully that's the case.

"I just want to play football as well as I can and it's up to other people to get it sorted."

Kilmarnock boss Jim Jefferies had no real complaints about the result, apart from the defending at the first goal which saw one of the smallest men on the pitch score with his head.

Jefferies said: "You will not beat Celtic if you gift them goals like we did.

"McDonald was the smallest player on the pitch and he almost got a second from the same situation.

"And Nakamura has done that to us and other teams before, although I didn't think it was a foul for the free-kick.

"But we kept plugging away and I can have no complaints about the effort and commitment."