Vardy came on as a second-half substitute to score his first competitive international goal and cancel out Gareth Bale's 42nd-minute free-kick, before fellow substitute Daniel Sturridge netted late to win it for England.
The arrival of Vardy and Sturridge lifted England, but the Leicester City striker insisted Hodgson gave the team no new instructions at the interval.
"We thought we were playing well, so the message from the manager [at half-time] was to carry on doing what we were doing and hopefully the goals would come, and that's what we've done," said Vardy.
England go into their final Group B game against Slovakia as group leaders with four points, and Vardy is now hoping he can force his way into Hodgson's starting line-up.
He said: "Everyone wants to be part of the starting line-up but it's a team game and there are 23 of us who all want to play.
"We'll wait and see. I'll be trying my hardest in training."
After a tense few days following the trouble that marred their opener against Russia in Marseille, Vardy also paid tribute to the travelling England supporters in Lens, saying: "The fans are brilliant. Everywhere we play the fans are nice and loud and they can be the 12th man for us."