The 30-year-old played the second 45 minutes but it remains to be seen if he will be fit to start against Croatia.
Victory over Romania means England have won both pre-tournament friendlies 1-0 but Southgate was not overly impressed with the performance.
He added: “Yes, we had chances to make it more comfortable but so did they, the first half we did not work hard enough without the ball, we were too stretched and did not press well.
“After half-time, I thought we improved and it was helpful we went to 4-3-3 later and I have to say it was a good exercise, players needed the minutes and learned a lot from the game. Good to win.”