Celtic have to move "more precisely" and "a bit quicker" in the transfer market, says manager Ange Postecoglou.
The Parkhead club signed Israeli winger Liel Abada and Japan forward Kyogo Furuhashi last week.
But both players are absent from the Champions League squad for Tuesday's first-leg second round qualifier against Midtjylland.
"We probably hesitated a couple of times and could have moved faster on some things," the Celtic boss 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."
Celtic have brought in four new players so far this summer, with Osaze Urhoghide and Liam Shaw coming in as defensive reinforcements from Sheffield Wednesday plus the arrivals of Abada and Furuhashi.
Reports suggest the the club have agreed a deal for Swedish centre-back Carl Starfelt but, with persistent rumours circulating about the futures of several key players at the club, Postecoglou concedes there is still a lot of work to be done on the recruitment front.
"It's a constantly evolving picture," the Australian added. "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."
McGregor to lead Celtic in 'new era'
Callum McGregor will lead the team out at Celtic Park in front of 9,000 fans for the first time since being officially announced as the club's new captain.
While his manager has "no doubt" about the Scotland midfielder's leadership qualities, McGregor puts much of that down to the "education" he received from his former skipper Scott Brown.
"I've had the honour to work closely beside him [Brown] and see how he operates every day," McGregor said.
"I just want to try and follow that as best as I can, then you need to put your own personality on it. It's a new era for the club, I'm desperate to get to work and make it a successful one."