Barnes and his Clarets side knew that victory at home to Newcastle United on the final day of the Premier League season would have kept them up and sent relegation rivals Leeds down to the Championship.
The two sides approached the final round of fixtures level on points but third-bottom Leeds had a goal difference of minus 38 compared to Burnley's minus 18.
It meant that out-pointing Leeds would have ensured Clarets survival but the Lancashire side were beaten 2-1 by the Magpies at Turf Moor and Leeds won by the same scoreline at Brentford.
Burnley eventually finished three points behind Leeds despite a strong late season resurgence under new interim boss Mike Jackson who was brought in to replace the sacked Sean Dyche midway through last month.
Barnes, though, said irreperrable damage was done at the start of the season as the Clarets took ten games to bag their first victory as part of a run that featured just one win in 21 games.
Despite being then offered late hope, Barnes admitted his side could have few complaints about being sent down.
"We can't use any excuses," said Barnes to Match Of The Day.
"It was down to ourselves at the end of the day.
"I think it was three wins in the first 20 odd (23 games) at the start of the season, that's definitely not good enough, from anyone.
"That's relegation right there.
"But we gave ourselves some hope and belief but it just wasn't to be come the end."