Former champions Argentina, Spain, Germany and Brazil all suffered shock group-stage losses and Africa, Asia and North America were represented in the last 16 along with traditional powerhouses South America and Europe.
Infantino said the matches -- "played in beautiful stadiums" -- had already attracted a TV audience in excess of two billion viewers.
"Fantastic atmosphere, great goals, incredible excitement, surprises, small teams beating big teams," he said in comments released by FIFA on Wednesday.
"Well, there are no more small teams and no more big teams. The level is very, very equal.
"For the first time as well, national teams from all continents going to the knock-out phase, for the first time in history. This shows that football is really becoming truly global."
Infantino has pushed through the expansion of the World Cup from 32 teams to 48 for the next edition, which will be held across 16 cities in the United States, Canada and Mexico in 2026.
FIFA was heavily criticised in some quarters for awarding the hosting rights to Qatar because of allegations of corruption and human rights violations.
Infantino rounded on European critics of the host nation in his pre-tournament address, accusing them of hypocrisy and adding that engagement was the only way to improve human rights.
Infantino said he had been delighted with the number of fans crowding into the stadiums and fanzones in the country and thought the final TV viewership figures would exceed five billion.
"At the end [of the day, we simply want to give some joy and some smiles to people all over the world," he added.
"That's what football is about, that's what the World Cup is about, and that's what should also happen from now until the end.
"We have already seen some great action on the field, which, (ultimately), is the most important part of what you do."