Wales' 3-0 win over Russia in Toulouse meant the Three Lions finish second in Group B.
Slovakia must now wait to see if they qualify as one of four best third-place best teams after their goalkeeper Matus Kozacik pulled off a string of saves -- some more luck than judgement.
England will now play their last 16 game in Nice next Monday against the side who finishes second in Group F, most likely against Hungary or Portugal.
It was at the Stade Geoffroy Guichard where David Beckham was sent off as England lost to Argentina on penalties in the last 16 of the 1998 World Cup.
Prince William, who turns 34 today, was in Saint-Etienne, sat next to FA chairman Greg Dyke who has said Hodgson will remain England manager -- provided they reach the semi-finals.
Hodgson's contract expires after Euro 2016.
The England boss boldly made six changes to team, starting strikers Jamie Vardy and Daniel Sturridge, who both scored off the bench in the 2-1 win over Wales.
Slovakia coach Jan Kozak kept faith with the starting side which beat Russia 2-1 last Wednesday.
Vardy worked hard throughout, but squandered two clear chances of England's nine first-half attempts on goal to Slovakia's single effort.
He fired over early on, then had his shot blocked by Kozacik in a one-on-one after winning a sprint against Slovakia captain Martin Skrtel.
And only a fine tackle from right-back Peter Pekarik denied Sturridge at the near post in the opening 10 minutes.
Lallana was then denied by Kozacik's reflex save with half an hour gone.
At the other end, only the slightest of deflections off Kozacik's shoulder kept out Nathaniel Clyne's shot.
There was a big cheer from travelling England supporters -- the loudest of the night -- when Wayne Rooney came on for Jack Wilshere with 56 minutes gone.
Dele Alli, on for Lallana, then saw his shot cleared by Skrtel after finding himself unmarked when he arrived in the area at pace.
Only England fans could be heard as the second half wore on, nosily urging the Three Lions on in search of the crucial goal which never came.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
