"Getting out of the group partly exceeded my expectations," Hodgson told BBC Radio 5 live.
"For us to get seven points with two victories and a draw probably exceeds everyone's expectations."
The 64-year-old continued: "We're very pleased to have won the group. It wasn't an easy group to win.
"Ukraine have very good players, France were undefeated in 23 games, and then there's Sweden who ended that run. But we deserve it."
A second-half header from the returning Wayne Rooney sealed England's passage to the last eight as group winners following a hard-fought win over the co-hosts in a Donbass Arena in Donetsk dominated by home support.
"It was always going to be a tough game," said Hodgson.
"We kept getting updates from the Sweden game and we knew France were losing, plus the fans were all behind Ukraine. It took a great effort from us to keep our shape and discipline.
Hodgson delight at England 'spirit'
"We thank the supporters, both the brave 4,000 here plus the people back home. All the vibes have been extremely positive, having a good feel-good factor. That rubs off on the team."
Hodgson praised goalscorer Rooney, who was playing his first game in the tournament after serving a two-match ban for his sending off in the final qualifying game against Montenegro.
"You know what Rooney can do, you know his qualities," said the England boss. "He gave an extremely disciplined performance, I think he and [strike-partner Danny] Welbeck worked extremely well together.
"I've played this down, but it was his first game in a while and the fact he's had 80 minutes in this match will fill him with confidence."
Graham TaylorIn Donetsk for BBC Sport
"In the main, throughout these three group games, we have had defensive stability. That has been our strength. We haven't dominated any of the three games we've played in.
"In tournament football you need good fortune, and England have had that. If we hadn't, another team would have. Ukraine were so much in control of the game, but they didn't have an end product."
Hodgson also paid testimony to captain Steven Gerrard, who set up Rooney's goal and was voted man of the match.
"You've got to single Steven out. I think to some extent he's been our man of the match in every match, it was a captain's performance," insisted Hodgson.
Hodgson admitted England enjoyed a slice of luck on Tuesday.
Ukraine not only dominated for long periods but were denied a perfectly good equaliser when Marko Devic's shot was several inches over the line before being hooked away by John Terry, but the goal was not given by the officials.
"We don't have goal-line technology, and even with slow-motion we can't be 100% certain. I'm led to believe the ball crossed the line, and that was a slice of luck," admitted Hodgson.
"But England have suffered in the past, and if there was a slice of luck, we got it."
By winning Group D, England avoided world and European champions Spain in the quarter-finals and will play Group C runners-up Italy instead in Kiev on Sunday.
"I'd have been quite happy to play the Spanish, but I'd rather miss them because they are the favourites alongside Germany," added Hodgson. "I think this team of ours would have given Spain a pretty good run for their money.
"The good thing is that we're there and we're not travelling home. There was not one person in our group who wanted to be on that plane tomorrow."
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