McInnes elected to stay with the Dons despite holding talks with the club  relegated from the Premier League.
His decision has "delighted" Brown, who is still an Aberdeen director.
"It would have to be an exceptional club before Derek would be tempted to go down south and have another interview," he told BBC Scotland.
"Sunderland was a unique situation, the Scottish connection may have been the reason that Derek went down.
"I genuinely believe that he's better than Sunderland and that he can get a fine job in the Premier League in England in the fullness of time."
McInnes, 45, replaced Brown as Aberdeen boss in 2013, winning the League Cup final the following year, the Dons' first silverware in 19 years.
In 2015, he and assistant Tony Docherty signed new contracts until 2019, and the club says the duo will now stay until at least that summer.
"Everyone I have spoken to are delighted that Derek and Tony are staying and the impact will be considerable," former Scotland manager Brown added.
"It looked to be a surprise, but I think that Derek would look to weigh up all the circumstances.
"I'm sure he sees, and he has stated, that there is unfinished work at Aberdeen.
"The big attraction to remain at Aberdeen would be the fact that he is almost guaranteed European football every year.
"And I guess it will be a while before Sunderland approach European football."
Aberdeen have finished second to Celtic in the Scottish Premiership for the past three years and were also runners-up to Brendan Rodgers' side in the Scottish Cup and League Cup last season.

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An investigation began following accusations of bullying and sexism towards top-level cyclists.
A report on its findings is due in May.
The head of British Cycling, Jonathan Browning, said checks were being added to protect against "behaviours that are inappropriate" to individual riders.
"The combination of new leadership team and structure, and the introduction of professional processes will ensure that we deliver on this promise," Browning added.
British Cycling published a 39-point action plan last month to address the draft findings of the independent review, commissioned in April 2016 by British Cycling alongside UK Sport, which provides elite funding to the organisation.
It came after former technical director Shane Sutton, who was was later cleared of eight of nine allegations, was found to have used sexist language towards cyclist Jess Varnish.
UK Sport chief executive Liz Nicholl says the independent review has "identified valuable lessons" for both British Cycling and other sports it funds.
Initially, key findings were meant to have been published in November. But the process has been delayed by legal wrangling, as those criticised have rejected the panel's findings. The process has also been criticised for not seeking a wider range of views.
Last month, British Cycling was warned it needed to do more to ease "concerns" over the way it is run before it can receive £17m. Grassroots sport funding agency Sport England said it wanted cycling's governing body to "meet the highest standards of governance" first. British Cycling will hold an extraordinary general meeting in July in a bid to vote through reforms.
Meanwhile, athletes are no longer being charged to lodge an appeal should they wish to contest their removal from the sport's World Class Performance programme.
Browning, who was elected chairman in February, is part of an overhaul of the leadership at the governing body, with the new performance director Stephen Park at this week's World Track Cycling Championships in Hong Kong, and new chief executive, Julie Harrington, starting in May. The organisation has also appointed its first 'people director', Michael Chivers.
Craig Brown believes Aberdeen manager Derek McInnes is "better than Sunderland" and it would take "an exceptional club" to tempt him away.
[NEXT_CONCEPT]
British Cycling has started work on the development of a code of conduct as part of its response to an independent review into the culture of the organisation.