Berahino lifted his shirt after to show a message that read 'RIP Love You Dad' after his first goal.
The message was dedicated to his father, who was killed in the Burundi civil war 10 years ago, but he was booked for the gesture and will now miss next Tuesday's game against San Marino.
Southgate said: "I hadn't realised he had been booked until he apologised to us at half-time. They are the rules and that's something we've got to learn.
"Hopefully it won't be too costly for us on this occasion. It was a personal thing but had we known we'd not have let him go out with it on his shirt. He is a good player and pleasure to work with."
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