England thumped Iran 6-2 with a fabulous performance, but the build-up to the match was overshadowed by controversy over the OneLove armband England's Harry Kane, and six other captains, were intending to wear at the tournament.
The wearing of the multi-coloured armband, in support of diversity and inclusion, was scrapped at the last minute by the English Football Association and the other associations under pressure from FIFA, who could potentially have instructed referees to show players' yellow cards.
On the eve of the match, Southgate had said he supported Kane's desire to wear the OneLove armband and was also asked by Iranian reporters about the ongoing protests in Iran.
Southgate said he had some sympathy for FIFA's stance but preferred to talk about his side's performance.
"I think every coach now deserves the right to be able to focus on the football and we understand there are a lot of issues that people want to want us to speak about," Southgate, whose side again took the knee before kickoff in support of anti-discrimination campaigns, told reporters.
"We've done that for 12 months, but this is a World Cup. We won't refuse to speak and we won't refuse to answer any questions otherwise answer anything. But the predominant part of my energy has to be on preparing the team."
FIFA's pressure to prevent captains wearing the OneLove armband in a country where homosexuality is illegal provoked a furious reaction from groups representing the LGBT+ (lesbian, gay, bisexual, transgender) community.
Southgate said it was down to the federations to deal with FIFA over the matter, not the players.
"Those discussions have been ongoing between several European nations and FIFA," Southgate said.
"Actually, I do understand FIFA's situation in that you can set a precedent and it's very difficult then, where do you draw the line? I think in an ideal world, that would have been a much clearer situation earlier.
"People know what we stand for, this group of players, we're taking the knee because it's something we feel we can make a difference with.
"There are some things that I'm not sure we're going to be able to make a difference with and therefore we should channel our energies in the right directions."
Saka Thankful For Support
Saka (21) was speaking to reporters after his two-goal cameo, and said the memory of missing in the shootout that saw Italy clinch the Euro title last year would be with him forever.
"But I am so blessed and so grateful to have coaching staff not only ... (manager) Gareth (Southgate) and the team at England but also at Arsenal, and my friends and my family put their arm around me ... and helped me to get back into a good place," he said.
"Every time I get the chance to wear the England shirt I always give 110% and do my best to make the nation proud."
Southgate was delighted with his side's thumping victory, but was also disappointed with the two goals they conceded.
"We're really pleased to start the tournament in this way and really pleased with our attacking play. We know that Iran usually are very difficult to score goals against," he told a news conference.
"I didn't like the end of the game. To concede two goals the way we did isn't the level that we need. So we're going to have to be better than we were today in certain aspects of our game against the USA because they're going to be coming for us full throttle, and we're going to have reset," he said.
While he acknowledged the difficulties for his players to keep their focus in a game that had a total of 26 minutes of stoppage time, Southgate said England would struggle to advance in the tournament if they allowed matches to drift again.
"It's a great start for us, it's a good platform to build on but ... there are things that we need to be better at if we are going to progress into the later stages," he said.
Southgate said defender Harry Maguire came off after feeling ill during the match but there were no other injury concerns.
