Kane went into the match as the tournament's top scorer but was left at the bench as Southgate shuffled his deck having already sealed a last-16 spot.
That result means England now face a tough test against Colombia in the knock-out stages, but Southgate believes he did the right thing.
"This was a game we wanted to win but the knock-out game is the biggest game for a decade so needed to make sure our key players were reserved," the manager said to ITV .
"The players tonight gave everything. We have seen the level everyone has been playing at, we need to keep improving.
"We kept pressing until the end. I think the supporters understand what the most important thing is."
Southgate also underlined his confidence in United striker Marcus Rashford, who endured a frustrating evening alongside Jamie Vardy in a revamped England attack.
"I think it is a pretty even game. They had better controlled possession and the best chances in the first half," he added.
"We had some good ones in the second half. It was a good test for us. It didn't happen for Marcus Rashford tonight but we don't suffer for it.
"We want to win football matches so we're not happy to come away being beaten."