Matthew Nicks says the Crows won't put a timeline on Dawson's return to action after his older brother Jaryd's death last week.
Dawson watched from the Adelaide Oval grandstand on Saturday night when the Crows banked a spirited one-point victory over St Kilda.
"It has been an emotional week, a really emotional week," Nicks said post-match.
"To get a win is a great result.
"When you spend time in a footy club like we are, you realise how lucky you are to be in a position like this when circumstances play out the way they did this week - in a really tough time for someone who means a lot to us and a family that mean a lot to us.
"So we're lucky. The footy club has done a great job, and it was good to have Daws here with the group."
The 45,854-strong crowd at Adelaide Oval stood as one in tribute to Dawson at the 12-minute mark - Dawson's jumper number - in the first quarter against the Saints.
And Nicks said the All Australian midfielder would be given all the time he wanted before returning to playing.
"We just get around him and the family and we will work with him on what's the right timing, there's no rush in that," he said.
"This is people first. Family is always number one, way before football, so we'll just work through it."
In Dawson's absence, former captain Taylor Walker emerged as Adelaide's match-winner in the 15.13 (103) to 15.12 (112) win over the Saints.
The 35-year-old Walker booted five goals, including the match-winner, in a display that carried extra significance.
"It's tough when your captain is not playing, but good to see a former captain step up," Nicks said.
"And I think there's a bit bit in it too: Tex is an emotional guy and he's doing whatever he could to sort of make Jordan proud."
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