The win - courtesy of Lucciano Becchio's early penalty - was Leeds' first in midweek for 364 days and they remain unbeaten since they were taken over by GFH Capital last week.
"Gary would have loved that, us getting stuck in, I thought it was fitting," said Warnock.
"It was a Gary Speed game tonight, roll your sleeves up and not shirking a tackle.
"We beat the top of the league on Saturday, but these (Leicester) are the best squad and you can tell that with the subs they made.
"But in both games we have deserved it. We played some good stuff, with flair, but also putting bodies on the line when we needed."
His counterpart Nigel Pearson said the Championship is a brutally tough league and Warnock agreed.
"Any one of the bottom six could go up. There's not one outstanding team," he said.