This week's departure of Jamie McGrath to Dundee United means Latics have now lost half a dozen players since the end of last term.
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With less than a month to go to the deadline, the Latics CEO says moves are afoot to address the balance.
"I think we'd always have wanted to have brought one or two more in than we have," he said.
"But the market is interesting at the moment, talking to other clubs and other agents.
"There doesn't seem to be that much movement, then you get a little flurry, and then it picks up.
"We've made one transfer in so far, there's another couple being lined up, but we'll continue to take our time and make sure we get the right players and the right characters.
"If you look at the team that was put together last summer, the overriding factor was character.
"There is an assumption, quite rightly, that they are footballers first and foremost, but you also look at the character right after that.
"And the results that came from having a good team and a good structure, full of integrity, were shown by us becoming champions at the end of the season."
Manager Richardson was again asked about the situation during his pre-Norwich press conference.
"We know our squad depth needs to improve, especially with the challenges ahead in the Championship," he said.
"Everything is a step up - players, coaches, managers, and depths of squads.
"Clubs are able to make five changes now, and that means some teams will be finishing a game possibly even stronger than what they started with.
"We'll be going into Saturday-Tuesdays quite quickly, and the challenges at this level are really heavy.”