The Manchester City forward netted a second-half winner to seal a 1-0 victory at Wembley on Sunday.
Sterling started ahead of Jack Grealish, Marcus Rashford and Jadon Sancho despite netting just three times in his previous 20 games for club and country.
He has now scored 13 goals in his last 17 England games following his Group D strike and repaid Southgate’s faith.
Boss Southgate said: “Raheem has had this hex in the tournaments and not being able to get the goal, I felt he was dangerous all day, right from the start he was a thorn in their side. I’m really pleased for all of them.
“He is a good player, his goal-scoring record suggests we should have faith with him, especially in the last few years.
“We know we’re going to need that depth. We’re going to need all those attacking players and there were a couple who didn’t get on today.
“We will need those guys through the tournament.”
Sterling latched onto Kalvin Phillips’ pass to fire past Dominik Livakovic from 12 yards and grab a 57th minute winner as England won a European Championship opener for the first time.
He told the BBC: “There are a lot of different reasons I haven’t scored for my club and that’s totally irrelevant now. I’m here with England, I’m enjoying my football and that’s the most important thing and I’m just happy to score.
“It’s great to get off to a win. Now we have the games to look forward to and hopefully go into them and win again.
“It’s been a long season for me, I couldn’t wait to get started with England and I knew it would be a positive one.”
Phil Foden struck a post early for the Three Lions and Phillips forced Livakovic into a smart save.
The Leeds midfielder impressed throughout but played down his influence on the international stage.
“I’m just laid back, it’s the kind of person I am, regardless of what is being thrown at me I take it in my path and try to relax as much as possible,” he told the BBC. “If I didn’t have the team and coaching staff around me it wouldn’t be possible.
“It was very enjoyable, it was very warm and took its toll towards the end of the game. I’m very happy with my performance but there are two more group games left.”