Ange Postecoglou admitted Celtic's need for new faces was clear to see after a pre-season defeat by Preston but Covid restrictions are making the task even more complicated.
The Australian handed Israeli winger Liel Abada a debut off the bench as 2,000 fans returned to Celtic Park for a 1-0 defeat by the Sky Bet Championship side.
But Kyogo Furuhashi earlier played one final game for Vissel Kobe – scoring a farewell goal – 24 hours after Celtic agreed a transfer deal with the Japanese club. And the Japan forward could take a further fortnight to get started with his new team.
Postecoglou had former Sheffield Wednesday pair Liam Shaw and Osaze Urhoghide in his starting line-up but other signings have not arrived quickly enough for Tuesday's opening Champions League qualifier against Midtjylland.
Celtic appear to be closing in on a deal for Rubin Kazan defender Carl Starfelt but the lengthy process of signing players is making their European push doubly difficult.
"We are working on multiple fronts," Postecoglou said. "It's pretty clear we need to bring players in.
"That's not an easy process at the moment but we are working hard and hopefully in the next week or so we can make some more announcements and bring people in."
On Furuhashi in particular, he added: "Unfortunately that's a challenge. It's not just about signing players, it's how we can get them in.
"It's a 10-day to two-week process so that's the challenging part at the moment, we're not able to get people in quick enough.
"It's just the world we live in. If we could get on a plane, go over there and do the signing, we'd all be taking photos and we'd be unveiling him here today. Unfortunately nothing like that happens any more."
With Christopher Jullien injured and Kristoffer Ajer absent again, Celtic had an inexperienced back line.
Ajer has had a fitness issue but he has been heavily linked with a move to Brentford and looks like he might have played his last game.
When asked about the Norwegian, Postecoglou said: "I'm concentrating on the ones who are involved. I can't afford to waste time on anyone other than the ones who are here and committed to being here."
Ismaila Soro, Ryan Christie and Nir Bitton were all absent but could be in contention to face Midtjylland, although James Forrest is a major doubt after returning from a 10-day self-isolation period.
Karamoko Dembele and Mikey Johnston were also absent after going off with injuries against Bristol City on Wednesday.
Vasilis Barkas was back in goal for the first half after suffering a finger injury in midweek and the Greece international made early stops from former Celt Scott Sinclair and Brad Potts.
Tom Rogic and Odsonne Edouard, who have both been affected by fitness issues so far in pre-season, came on for the final half hour along with Boli Bolingoli and Abada.
Preston soon scored from Ben Whiteman's penalty and were worthy of their lead, but Abada, Rogic and Ewan Henderson all threatened as the hosts rallied.
