Fresh investment and renewed partnerships have reinvigorated the team in recent seasons after a period which saw it languish towards the back of the field.
And while the team has re-emerged at the front end of the midfield, Brown suggests some key developments within the operation need to come online before further steps can be expected.
“We've been on this journey of, when I joined, we've gone ninth, sixth, fourth, third, and here we are in the third [in the constructors' championship],” he explained.
“It gets tougher as you get closer to the front, so I don't think it's going to be two, one; that would be nice, but I don't think that'll happen.
“I think while we now have the annual resources to compete at the same level as everyone else, we are behind on our infrastructure, and while we've let loose the investment, it's simply going to take time.”
Key among the infrastructure currently under construction is a new wind tunnel, though it will not come online in the near future.
Instead, it's an investment into the team's future competitiveness with the squad having to deal with what it has for the moment.
“We're in one of the less technically developed wind tunnels, unfortunately, and that's a huge disadvantage,” Brown explained.
“I think we'll have no excuses come the 2024 season, and we'd like to think at that point the sport is going to be so competitive that there'll be a variety of teams fighting for the championship. I'd like to think we'd be one of them.”
There has been other investment made off-track too.
Earlier this season the team refurbished the Brand Centre, the motorhome it takes to European events.
The revised complex debuted at Monaco having undergone work to make it more sustainable and carbon friendly, points in-keeping with McLaren's broader corporate targets.
“And we have other stuff that you'll see later in this year that will become visible that you'll see our investment,” said Brown.
“But we really won't be, in our opinion, caught up on our infrastructure until the 2024 car comes out.
“So I think until then, we will be doing the best we can with the equipment that we have.
“Until we get caught up, I think it will be difficult to think that we could beat those guys [ahead of us] in a straight-up fight.”
It has been hoped that new rules set to be introduced next season will shake-up, or at least close, the pecking order.
Red Bull and Mercedes currently enjoy a sizeable advantage over the likes of McLaren and Ferrari, who are locked in battle for the best of the rest tag.
Brown however isn't expecting a revolution, suggesting surprises like what was seen in 2009 are now next to impossible.
“You never know with the new formula who's going to get it right, who's going to get it wrong,” he said of the 2022 ruleset.
“Brawn obviously punched above their weight when they won the championship and they weren't the biggest resourced team, but also I think the rules are so much tighter now to come up with a big clear advantage like that.
“I think in today's world is going to be more difficult.
“So we're going to give it our best shot, but I think we should manage expectations that it's going to get tougher from here on out.”
Lewis Hamilton won McLaren's last drivers' title in 2008, while its last constructors' crown came in 1998 (it scored enough points to win the 2007 title but was scrubbed from the competition and fined $100 million after being found with confidential Ferrari intellectual property).