On a night marred by racism from the Puskas Arena stands, the Three Lions kept their heads and ran out 4-0 winners to maintain their winning start to Group I.
Just 53 days on from the penalty shoot-out loss to Italy in the Euro 2020 final, Southgate named 10 of the side who started at Wembley on July 11.
Grealish was the only player to come into the team and the new Manchester City signing caught the eye with an impressive display.
Asked if he was happy with Grealish’s ability to create chances, the England boss replied: “Yes, absolutely.
“But also the angles of his pressing and the way he chased the ball down because that helped us to turn the ball over high up the pitch.
“We know that when he is in possession of the ball he has got that ability to find a pass when he is on the run and take people out of the game individually – so I thought his performance was very, very good.”
On a difficult night, with no travelling supporters officially among the capacity crowd, England’s pre-match taking of the knee in the now-familiar anti-racism and discrimination stance was roundly jeered.
During the second-half, monkey chants could then be heard, reportedly aimed in the direction of Raheem Sterling – who opened the scoring – and substitute Jude Bellingham.
Southgate praised the way his players dealt with the hostility from the fans but was also delighted with the way they dominated a team who had held France and Germany to draws here during the group stages of Euro 2020.
“I think we played very well, the players have really applied themselves well,” he added.
“Their pressing when we lost the ball was excellent right through the team and they were on the front foot, winning any balls that were played up to the opposition’s forwards so we made it difficult for them to get out and breathe in the game.
“Then in the main we used the ball very well, a couple of times a little bit of sloppy play, but it looked like the only way they were going to score was a counter-attack or a foul conceded from a counter-attack.
“But I was really pleased with the level and the players deserve huge credit for that.”