Parker has kept a close eye on developments at the Stadium of Light this summer after Sunderland won promotion to the Premier League with his Burnley side last season.
The Clarets came out on top as the promoted sides met at Turf Moor on Saturday, and while Burnley were up against a largely new-look Sunderland side, there was a lot that Parker recognised about the Black Cats.
"It was different in terms of personnel but the main structure of their team is probably very similar," he said.
"There's not much \[different\] in terms of the way they play and their structure. But look, they've recruited very well, they've spent an awful lot of money and they've brought in some very, very good players.
"So, yeah, I think there was more of a challenge identifying their key players or their key traits and what they bring. In terms of structure-wise, it was very, very similar."
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Parker was thrilled with the three points against Sunderland, secured thanks to second half goals from Josh Cullen and Jaidon Anthony.
Burnley's boss was frustrated with the decision to rule out Lyle Foster's first half goal but got the reaction he wanted from his side after the break.
He said: "It was disappointing with the goal that obviously didn't stand for us. It was quite soft.
"We got off to a great start in the second half. Our structure today was very good. I thought we defended very, very well.
"And then we hit them on the counter. It was a lovely finish from Jaidon, which probably gave us some oxygen, to be honest with you. Like always in these games, 1-0, pressure's coming, they can commit more men.
"And we needed to soak it up, which we did very, very well. It was diligent. And then obviously hit them on the counter, which gave us some air."
Parker added: "I'm delighted, really. I'm absolutely buzzing, first and foremost, for the players and for the fans and everyone involved. I thought we were brilliant today.
"I thought it was everything we were going to need to be.
"It's obviously a big chance early on \[for Mayenda\] with a great save from Martin.
"I asked the lads today to show a real endeavour, to show an impetus, to get the supporters right behind us. And I thought we did that. We were well worthy of the three points."