England kicked off their World Cup campaign with a commanding 6-2 win over Iran at Khalifa International Stadium on Monday as Jude Bellingham, Bukayo Saka (twice), Raheem Sterling, Marcus Rashford and Jack Grealish all found the net.
It was England's biggest-ever victory in their opening match of a major tournament but Southgate was concerned about a second half in which Mehdi Taremi scored twice, the first a superb first-time finish and the second a stoppage-time penalty after a debatable intervention from VAR as John Stones pulled Morteza Pouraliganji's shirt.
"Look, we are really pleased to start the tournament in this way, really pleased with our attacking play," Southgate said in his postmatch news conference.
"We know that Iran usually are very difficult to score goals against so it is a credit to our players, their movement, the quality of our passing, the quality of our finishing.
"I didn't like the end of the game. To concede two goals the way we did isn't the level we need. We are going to have to be better than we were today in certain aspects of our game against the USA because they are going to be coming for us full-throttle and we are going to have to reset.
"I don't like games that drift as this one did and it was difficult because there was so much added time in both halves. I understand the focus drifting a little but that won't be enough for us to progress in the tournament. So, we've still got a lot to do to qualify but of course this is a really good start for us."