Martin O'Neill insists there is "no question" that Celtic will make more signings this summer, but he wants "quality rather than quantity".
The Scottish Premiership champions have brought in Camilo Duran and Kasper Hogh so far, with Alex Oxlade-Chamberlain returning on a new one-year deal.
Supporters have been frustrated by the club's lack of transfer activity, while influential striker Daizen Maeda has left to join newly-promoted Premier League side Ipswich Town.
Celtic begin their title defence against Dundee on August 3, live on Sky Sports, ahead of their Champions League play-off later this month.
But manager O'Neill is urging some patience from fans.
"We're trying to get some quality into the football club," the 74-year-old told Sky Sports News.
"We've lost Daizen, he was a big, big player for us and so we have to replace him. I think that we're doing our best to do that.
"We will get some more players in, there's no question about that, but I want quality rather than quantity."
After a rollercoaster campaign that saw O'Neill return to the club twice, Celtic clinched the title in a final-day decider against Hearts in May.
And O'Neill wants the players to take some lessons into the new campaign.
"Last season was terrific, it's gone now, it's consigned to history. Now we're ready to go," he added.
"I think it was mentality as much as anything else that got us over the line.
"It was strong, it was a will to win and we saw it through.
"That will be very, very important this season, there's no question about that."
McGregor: Where I want to be
Meanwhile, Callum McGregor has reiterated that Celtic is "where I want to be" amid ongoing speculation linking the long-serving captain with a reunion with former boss Brendan Rodgers at Al Qadsiah in Saudi Arabia.
The 33-year-old said in April he wanted the club to match his ambitions if he was to stay on as they laboured towards the Scottish Premiership title.
"Listen, this is a football club that's been part of my whole life since I was eight, nine years old. It's where I want to be. It's where I want to play football," he said.
"Ultimately, I want to keep driving everything that I possibly can to make sure this club is successful. Then eventually, the day that you do leave it, you want to leave it in a really good place."
Asked if he felt the club were matching his ambitions, McGregor said: "Yes, listen, we've signed two strikers, two really good players. Obviously, they've come in and done really well.
"Big Kasper (Hogh) has just joined us over the last 24 hours. It's good signs, it's positive steps and that is to add to what is a really good group already.
"I spoke about this at the end of the season as well. I don't really think there's a group of players and a group of staff that could have got us through that difficult moment as much as these boys did.
"It's obviously about trying to add bits of quality, but what we do have here is guys who want to work for the club, who are good footballers, who want to get better and ultimately did bring success to the football club during a difficult season, so we have the makings of a really, really good team.
"Obviously, the standard for us is trying to get to Champions League football. That's where we want to be. It takes the club to a different level. So, can we keep pushing as players, staff and our football club to make sure we get there?"
Celtic begin title defence against Dundee
Celtic begin their Scottish Premiership title defence at home to Dundee on August 3, live on Sky Sports.
The Monday night clash, which will kick-off at 7.30pm, rounds off a groundbreaking opening weekend that will see all six top-flight games shown live on Sky Sports for the first time.
Click here for all of Celtic's Premiership fixtures, including dates of the first Old Firm clash this season.