The Wallabies opened their Investec Rugby Championship campaign with consecutive losses to New Zealand and were on the wrong end of a 38-12 hammering against the Springboks in Brisbane last month.
They finally posted their first win of the McKenzie era with an unconvincing 14-13 victory over Argentina in Perth on Saturday night.
McKenzie's men will reassemble in Sydney on Saturday before embarking on their two-Test tour of South Africa and Argentina, and the coach is confident of more success on the road.
"You can get bogged down in how people want to describe things but I've definitely seen progress in parts of the game, but there are parts that we need to do better at there's no doubt about that," McKenzie said.
Pressed on his side's hopes of avenging their last-start loss to the Springboks, McKenzie replied: "We just played a little bit too laterally [in Brisbane] and we had other ideas which we never quite got to.
"We just sort of got stuck in lateral mode but we were competing, if you remember the game it was 19-12 and I think Christian Leali'ifano dropped the ball after we made a line break so if you go 19-all with 20 minutes to go that's a different game.
"Instead they scored two tries and we missed ours and they ended up with a handsome score line.
"It's not like we're way out of their league, you've just got to make sure you get those moments right."
McKenzie stressed the importance of muscling up against the Springboks pack after losing the physical battle in Brisbane and concedes all nations are still coming to terms with the new scrum laws being trialled in The Rugby Championship.
"It is very different with the hooker striking, it sounds simple but there is a lot of different mechanics in there at the moment so it's not so simple just to suddenly go out there and do it differently," the former Test prop said.
"Some teams have adapted better, there's a lot of subtle stuff that [is] going on as people work through it from a coaching point of view and look for opportunity.
"If you look across Europe a lot of teams are doing different things, so we're in that sorting out period.
"I think by the time you get to the end of next season and the European clubs have had a crack at it someone will work out the best way to take advantage of it and no doubt the referees will go and tweak it again anyway."
Veteran looshead prop Benn Robinson is back in the fold after being overlooked for the previous four Tests at the expense of Brumbies youngster Scott Sio, while skipper James Horwill has been named to return from a hamstring injury.