Before England’s 1-0 friendly win over Romania at the Riverside Stadium, TV pundit Roy Keane suggested Henderson shouldn’t be in the squad as the Liverpool captain hasn’t played a competitive game since February due to a groin injury.
Henderson returned to action against Romania as he replaced Kalvin Phillips at half-time.
Marcus Rashford scored the only goal of the game with a second-half penalty, yet Henderson squandered another chance to score from the spot when his effort was saved by goalkeeper Florin Nita.
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When asked about Keane’s comments and Henderson’s penalty after the match, Southgate said: “Well I think firstly we are not distracted by anything.
“We know the situation Hendo is in, he’s been a very positive influence around the camp with the group.
“It’s a step forward for him physically today which was important for him to be able to play some sort of part in the tournament and we are realistic about what that could be.
“It’s not a situation where it’s dividing the group or it’s unrealistic what’s possible.
“We’re not hanging our hat on him being fit and if we can get him to a good level then that’s a bonus. We’ve got 26 players which hasn’t been the case before.
“With the penalties we are very diligent in how we practise them. I didn’t expect what happened to happen and I wouldn’t expect that to happen again.”
England are also monitoring the fitness of Harry Maguire, who is recovering from an ankle injury and hasn’t played since suffering the setback on May 9.
When asked about the Manchester United captain, Southgate added: “He’s progressing well, he was running today.
“The last few days have been very positive, there is still a little bit of work to be done but he's definitely heading in the right direction and we were very pleased with the progress in the last two days in particular.”
England now have a week to prepare ahead of their Euro 2020 opener against Croatia at Wembley on Sunday, June 13.