Leicester's impending drop to the Championship was confirmed on Sunday after a 1-0 loss to Liverpool - their 23rd league defeat of the season.
Defeat at the King Power was also their ninth straight match at home where they failed to score, which is a new English record.
Vardy, who led Leicester to the Premier League title in 2016, is their top scorer in the division with just seven goals, but hasn't netted in any of his last 10 outings.
In a no-holds-barred assessment of Leicester's season, Vardy labelled the campaign a "s**t show" while admitting the team "failed" as a collective.
"At this point, I don't even know what to say," Vardy said in a statement posted on social media.
"No words I have can ever express my feelings of anger and sadness with the way this season has gone. There are no excuses.
"Collectively, as players and as a club, we failed. There is simply no hiding, and I refuse to entertain any suggestion of doing so.
"Having been at this club for so long, we've experienced so many highs and successes, and this season has been nothing but miserable, and for me personally, a total embarrassment. It hurts, and I know you’re feeling it too.
"To the fans: I'm sorry. Sorry we haven't performed, and sorry we end the 2025 season with such a s**t show."
Vardy, 38, is in his 13th season with Leicester, which could be his last with his contract expiring in the summer.
The striker is likely not the only name at Leicester whose future is up in the air, with manager Ruud van Nistelrooy also expected to be under scrutiny.
Van Nistelrooy took charge in November and has only taken four points from his last 18 games, despite taking four in his first two.
Leicester have five games remaining this term, starting with a trip to the Premier League's form side, Wolves, on Saturday.