Asked about the ban following talks with Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al-Thani, Blinken said: "It is always concerning when we see any restrictions on freedom of expression, especially when the expression is diversity.
"No one on the football pitch should be forced to choose between supporting his values and playing," he added.
The armbands had been viewed as a symbolic protest against laws in World Cup host Qatar, where homosexuality is illegal. FIFA's move has been criticized in Europe.
Speaking in Doha hours after watching the United States held to a 1-1 draw by Wales, Blinken told a press conference that no team should be forced to choose between "supporting his values" and playing.
England, Germany and five other European teams abandoned plans to wear rainbow-themed "OneLove" armbands at the World Cup because of the threat of FIFA disciplinary action.