Oxlade-Chamberlain, 18, became the second-youngest England player after Wayne Rooney to appear at a European Championship when he faced France on Monday.
And he impressed in the 1-1 draw.
But dad Mark, who won eight caps for his country, only just saw the kick-off after his holiday flight from Portugal was delayed.
He said: "I found out about half an hour before the start Alex was playing.
"I had a 24-hour delayed flight and we only got back about 4pm, so had to watch it at the Hilton Hotel at Gatwick. It was frustrating but we watched all the game.
"It was good to see. It was a fantastic achievement for him and, hopefully, not the last.
"I'm always critical but I congratulated him. I thought he did well, along with the rest of the team.
"I think he was more critical of his performance than I was. He seems to take everything in his stride at the moment."