Toney made his England debut for the final 10 minutes as Southgate's side made it two consecutive wins in qualifying with a 2-0 victory over Ukraine at Wembley on Sunday, sealed by first-half goals from Kane and Bukayo Saka.
The Brentford striker is facing an anxious wait to discover if he will be hit with a lengthy ban for over 250 alleged breaches of the Football Association's (FA) gambling rules, and has competition to be Kane's deputy from Ollie Watkins, Callum Wilson, Tammy Abraham and others.
Asked if he has done enough to establish himself as England's second striker, Toney said: "I hope so. I hope I keep performing and keep myself in and around the mix.
"But there’s Harry Kane, one of the best strikers in the world, in front of me. And there’s other strikers around the Premier League that are doing well as well. I’ve just got to keep doing me and hopefully it’s enough.
"All I can keep doing is keep working hard, and when my chance comes, take it with two hands. I did that last night. Thankfully I got my cap, and it means a lot — believe me.
"It feels so surreal. I couldn’t think of a better ground to do it in. For me and my family, it’s been a long journey, but to finally make it onto the pitch is a massive moment. Of course, I was itching to get the ball in the back of the net. But the main thing is to do things right, see the game out, and get three points.
"I feel like I have [impressed Southgate]," he added. "I work on my game every day. On the training pitch I’ve been working hard. When you’re not playing, you’ve just got to do that."
The 27-year-old's debut capped a remarkable rise for a player who was in League One with Peterborough just three seasons ago. He became the first Brentford player since 1939 to earn a cap and the first ever graduate from Northampton Town's academy to represent England.
"I was literally saying to my friend the other day [that] three or four years ago I was fighting for promotion at Peterborough and now I’m making my debut for England," said Toney, who has scored 16 times in the Premier League this season, bettered only by Erling Haaland and Kane.
"It’s been a massive, long journey but to finally get my first England cap is a massive achievement. The hard work starts now. A hundred percent [I thought I could do it]. You’ve got to dream big, and I’ve made my dream a reality."
He added: "Everyone at Brentford are rooting for me. I was getting messages before the game. I got the cap, so it’s a special moment for myself, everybody at Brentford, and everybody involved. And I'm a Northampton boy, Northampton-raised, so it’s a big achievement for everybody at Northampton, too."
Kane extended his lead as England's record scorer with a 55th international goal, a tap-in at the back post from Saka's cross, and the Arsenal winger scored a magnificent second three minutes later.
Ukraine captain Oleksandr Zinchenko believes his Arsenal team-mate is currently among the best players in English football.
"Definitely he is one of them, that’s for sure," Zinchenko said. "I hope he will be on this form until the end of the season because he’s such an important player for us. Everyone knows this. He is an amazing player. He is on fire at the moment. There is no friends on the pitch. Unfortunately he beat me."