Arena, who oversaw USA's failure to qualify for the World Cup from the CONCACAF section in which Mexico triumphed, was impressed by how they restricted Germany, but expects the usual suspects to reach the latter stages.
"Naturally, Mexico had a very good performance against Germany, upsetting them with a 1-0 victory," Arena told Omnisport when promoting his new book.
"One would think they're in good shape to qualify out of group play and be in the round of 16.
"They had to defend with a lot of numbers for a lot of the game. That's not really Mexican football, but they were all committed to do it and did an outstanding job.
"At the end of the day I don't think there's going to be many changes or surprises in this World Cup. When all the smoke settles I think you're going to see all the big boys that are usually there in the end."
Panama dramatically denied USA a place at Russia 2018 and lost their World Cup debut 3-0 to Belgium, with Arena predicting similar results in their remaining fixtures.
"You know the U.S. beat them 4-0 at home in game nine of the Hex, we drew with them in Panama. They're probably a team that's going to have a difficult time at the World Cup and not get out of the group play."
The USA will host the 2026 World Cup alongside Mexico and Canada after their joint bid was selected at last week's FIFA Congress in Moscow.
MLS was born out of the USA hosting the 1994 edition and Arena believes the return of football's grandest competition will have a positive effect on the domestic league and its players, though he thinks new initiatives are needed to maximize the potential impact.
"Having the World Cup in the US in 2026 is going to be terrific for our country, for our soccer environment. It's going to bring much more attention to American players, to our league and help to continue to grow the sport," he added.
"I think between now and 2026 we can make a bunch of changes in our country to help grow the sport and hopefully over the next couple of years we get a little bit creative, we set some good policy and we succeed with it."
Outspoken, honest, and game changing—Bruce Arena’s memoir What’s Wrong with US? is available now wherever books are sold. For more information, visit https://www.harpercollins.com/9780062803948/whats-wrong-with-us/.