The Nets signed NBA All-Star duo Durant and Irving to go with the likes of DeAndre Jordan, Garrett Temple and Wilson Chandler.
Atkinson, who has been at the helm since 2016, said the signings were huge for Brooklyn.
"I use the word humbled that guys of that calibre would choose to play with us," he told a news conference on Tuesday.
"The biggest credit goes to our returning players – Joe Harris, Jarrett Allen, Caris LeVert.
"I think, at the end of the day, all our free agents, Garrett Temple and DeAndre, they looked at it and [said], 'man, those are guys we want to play with'."
While Durant is set to miss most, if not all, of the 2019-20 season due to an Achilles injury, the Nets look well-placed to reach the playoffs for the second straight campaign.
Brooklyn finished 2018-19 with a 42-40 record before losing to the Philadelphia 76ers in the first round of the playoffs.
Atkinson believes the Eastern Conference will again be tough after several big moves in the offseason.
"I think we've added some really good players and our goal is just to continue that rise," he said.
"I think there are going to be a lot of good teams in the east, I think there is going to be a lot of parity, that's my gut.
"Jimmy [Butler] going to Miami, geez that makes them better, Philly with all their big guys and shooting, Boston sign Kemba [Walker], we all know Kemba. I see a lot of parity in the east."