Ange Postecoglou admits Celtic have “hesitated” in the transfer market and his urged the club to work quicker.
Liel Abada and Kyogo Furuhashi were confirmed last week but neither will be available to face FC Midtjylland tomorrow night.
And Postecoglou wants future deals to be concluded more swiftly with the understanding that there are likely to be delays in getting players into the country.
"We probably hesitated a couple of times and could have moved faster on some things," he said.
"That hasn't helped us. In normal circumstances these processes are fairly straightforward. Get a player, sign him, take him on a plane, take a photo and away he goes.
"That process is now taking two to three weeks. That's where we've got to move a little bit more precisely, understand there's going to be lag time and move a bit quicker."
A deal for Swedish international defender Carl Starfelt is thought to be close although he too would have to go through a period of isolation before he was available.
The futures of Kris Ajer, Odsonne Edouard and Ryan Christie are still unclear and Postecoglou admits there is still plenty of work to be done on recruitment despite the start of the Premiership season being just around the corner.
He added: "It's a constantly evolving picture. What I do know is we need to bring in a certain number of players. It doesn't take a genius to figure out.
"When I look at the squad we are still very light in areas, just for depth more than anything else. If we want to challenge on all fronts we need a strong squad. At the moment I don't have that."
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