Ruud Gullit believes Celtic have to start punishing their European rivals if they want to cement their status as contenders for the later stages of the Champions League.

The former AC Milan playmaker watched his old side struggle against Neil Lennon's Scottish champions at home last week yet still emerge with a 2-0 win.

Despite dominating the seven-time European champions in the passing stakes, Celtic failed to turn their possession into goals and were eventually sunk as Cristian Zapata and Sulley Muntari struck twice in the final 10 minutes for the Rossoneri.

Gullit - who was speaking at Gleneagles Hotel, Perthshire, as he promoted next year's Ryder Cup - said: "I saw the Milan game, Celtic had unbelievable opportunities to score goals but they didn't do it, because of quality.

"Any little chance Milan get, they will score. That's the reality of being in such a big competition.

"Celtic in Scotland get loads of chances to score and if they miss one that's okay, but not in Italy.

"Milan lost (on Sunday) at home to Napoli because Napoli took their chances. Celtic were as good and at some points better than Milan, but they missed their chances."

Gullit also starred for Celtic's other Group H rivals Ajax during his glittering career and insists the double-header with the Dutch champions on October 22 and November 6 will be pivotal to both teams' hopes of qualification for the last 16.

Frank de Boer's side has shipped eight goals in two defeats to Barcelona and then domestic rivals PSV Eindhoven in the past week but Gullit still believes the Glasgow side will have to work hard to overcome the Amsterdammers.

"It looks like the most important games will be between Celtic and Ajax so I'm looking forward to that," said the former Chelsea boss. "Ajax have proved to do well against British teams recently so it's going to be interesting.

"They have had two big defeats in the last week against Barcelona and PSV so they have been knocked down a little bit so lets see how they do.

"Ajax just lost important players at the end of the transfer window. It's a ridiculous system, they played three times in the domestic league then sold two players and they have not been able to cope with it.

"The matches with Celtic will be even I think - they play different styles of football but that's good so I'm looking forward to those games."

Milan's 2-1 defeat to Rafa Benitez's Napoli on Sunday was further evidence that they are not the force of old but Gullit still sees them following Barcelona into the knock-out stages.

"Barcelona are favourites for the group and everybody thinks AC Milan will join them, but they also lost yesterday," said the 66-time capped Dutchman.

"They have their difficulties but it will be hard for Ajax and Celtic to qualify."