Andreas Hinkel and Nakamura appeared the most likely players to carve out an opportunity.
And Rangers' Kyle Lafferty was fortunate not to be sent off for a lunging challenge on Andreas Hinkel.
Celtic took the lead within the opening 30 seconds after Andrew Driver's poor clearance was collected by Andreas Hinkel.
"I think we can do it because I don't see a strong team like Arsenal in this competition, " said Hinkel.
Mowbray expected Andreas Hinkel and Paddy McCourt, both left out the team, to be fit to face Rangers on Sunday.
Celtic forged ahead after 21 minutes through Loovens after United skipper Lee Wilkie had conceded a corner defending an Andreas Hinkel cross.
Mizuno headed the third from an Andreas Hinkel cross after the break.
Andreas Hinkel set up Scott McDonald's 39th-minute strike for the opener. and seven minutes into the second-half Samaras nodded in a close-range header.
The Celtic manager admitted that it was a blow to lose regular full-backs Andreas Hinkel and Danny Fox to injury before the game.
However, there was no place in the squad for Aiden McGeady, with a back injury blamed for his absence, while Andreas Hinkel was also omitted.
And Hinkel expects the German side to be Celtic's toughest opponents.
Celtic already have Andreas Hinkel and Mark Wilson as cover at right-back, but Lennon has been suitably impressed by the player who has 50 international caps.
Mr. Hinkel, the high-rise's developer, said 19 slabs of the wall, each four feet long, will be relocated "only a few meters" beside the East Side Gallery.
Andreas Hinkel and Mark Wilson are out of contract at the end of the season and manager Neil Lennon has moved to increase his options at full-back.
BBC: Cardiff full-back Matthews signs pre-contract at Celtic
It is unclear what legal grounds protesters would employ to halt removal of the wall section, given that the local district has granted Mr. Hinkel's company permission to proceed.
Mr. Hinkel said he is for now stopping work to remove the stretch of wall so he doesn't further stoke tensions, and to have a chance to have discussions with city officials.
Substitute Fortune was on the pitch less than 60 seconds before he latched on to a Hinkel long ball and thundered in an unstoppable shot to put Celtic back in the driving seat.
The stalemate was broken six minutes from the break when Hinkel latched on to a ball on the right-hand side and sent in a low ball for McDonald to fire past Langfield for the opener.
Conroy appeared to have got that call right despite the resulting anger from the home support, but he was too lenient 11 minutes later when only producing a yellow card after Lafferty lunged dangerously, studs-first into Hinkel's shin.
Celtic's speed and movement was a delight to watch, but Rangers' doggedness was denying them threats on goal until a fine Hinkel cross was met by the head of Barry Robson and looped from 15 yards off the face of the crossbar.
The building's developer, Maik Uwe Hinkel, said the relocation of a section of the wall is necessary not only to allow street access for the luxury tower, but also is demanded by the city to allow access to a planned waterside park and bridge for pedestrians and cyclists.
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