Last round, Wright played his first match since tearing his ACL while playing for Australia in South Africa in August, and he impressed on his injury return.
The 28-year-old provided two try assists in a silky display but the Brumbies fell at home in a shock 33-28 loss to Fijian Drua.
He played around 60 minutes against the Drua but hopes to see out a full match this weekend.
"I hadn't done it for eight months or whatever it's been since I've played a game, and the lead-up was super exciting," Wright said.
"Result aside ... stoked to be back and almost happier that the first game's out of the way and then everyone can stop talking about it now."
Wright was relieved to turn the focus to the competition's inaugural Super Round in Christchurch, where the fifth-placed Brumbies will tackle the second-ranked Hurricanes.
The teams meet in the first match on day two on Saturday, with the three-day, five-game, Anzac showpiece opening the indoor One NZ Stadium.
A win over the Hurricanes would make the Brumbies the first Australian Super Rugby outfit to beat all five New Zealand sides in the regular season.
Wright said while the sweep was a goal his team wanted to tick off, returning to their best form was just as important after two defeats to the Drua as well as home losses against the Waratahs and the Reds.
"If you asked us if we were to lose four games in the first 10 rounds, which four would we have lost, you probably wouldn't have mentioned the ones that we have lost, right?" he said.
"If we were to be really honest with ourselves, that's something that we sort of kick ourselves on at the minute.Â
"If we can beat the Canes this week, we beat all the New Zealand teams and that'd be great but we're not sort of focused on an external stat like that.
"The boys have laid such a great platform in the first little bit of the season and we've got to pick back up. We've dipped off in the last little bit where other teams have started to hit their strides."
