The Three Lions hit their opponents for six in Monday afternoon's clash, but conceded twice in the second half.
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England's victory was Southgate's ninth at a major tournament, with the ex-Middlesbrough gaffer overtaking the tally of the legendary Sir Alf Ramsey.
And while Southgate was delighted by England's attacking prowess, he has insisted they must 'be better' in their next outing against a talented and youthful US side.
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Speaking to talkSPORT's England correspondent Fare Carruthers about his team's performance, Southgate said: "Look I'm really pleased with the three points.
"And I'm pleased with our attacking play, but we were sloppy in moments and we could have conceded in the first half.
"And we've conceded two poor goals in the second, so we're going to have to be better than that.
"I've got to balance how pleased I am with the approach of the whole squad - which has been brilliant all week.
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"We felt we would get a good performance today, but we're going to have to be better than we were for 95 or 100 - however many minutes - we're going to play next game.
"Because the States will be out the traps so quickly, and when a game peters out like that, I don't like it, because it's not good preparation for the next one.
"We'll have to hit a quick reset button."
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Southgate though was thrilled by the dazzling displays from youngsters Bukayo Saka and Jude Bellingham.
England face the USA in their second game on Friday at 7pm, which you can listen live to on talkSPORT.
Commenting on the duo, he remarked: "I think they've benefitted from being with us for quite a period of time now.
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"And of course Bukayo ended up starting a lot of games for us in the last Championship [Euro 2020].
"So they're both used to now being in our environment, and they're really exciting young players.
"They both work so well for the team, they've got a modesty and a humility about the way they play and the way they carry themselves.
"I think that is what we have with this group of players - the whole squad - and we've got to make sure that today is just the start point and that we show that humility now in how we go about our work."
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