Harriers' play-off hopes were finally dashed when they lost 3-0 to Mansfield and Luton won 2-0 at champions Fleetwood in today's end of season finale.
However, the Aggborough outfit finished sixth for the second season in a row and topped last campaign's efforts by taking their promotion chase to the last game of the season.
Burr and Whild have guided a young squad through a testing 46-game campaign, despite season-ending injuries to Danny Lewis and Tom Sharpe as well as the loss of striker Jamille Matt who is dealing with his work permit issues.
Harriers pushed the likes of big-spending Luton, York and Mansfield on a much smaller budget compared to their rivals.
"Put into perspective there's two things. Losing today was disappointing but the second is the season itself," commented Whild.
"To take it into the last game and finish sixth again and certainly move on with the players we've got here is a fantastic acheivment.
"It doesn't take away the disappointment of losing but you've got to give respect to Mansfield, you can see they're on a good run of form.
"You've only got to look at the clubs in the play-offs, York, Luton, Mansfield and Wrexham - massive clubs. For us to take them all the way with our resources is good.
"They talk about managers of the year and to be fair to the gaffer, to take us this far for two years running is absolutely fantastic.
"We try to play football and entertain and I think we've done that this year.
"We've had a great season again but that doesn't take away the disappointment from myself, Steve, the players and everyone at the club, because we wanted to get into the play-offs and were disappointed with the result.
"It's great to come this far with a young group of players who I am sure will be better for the experiences of the season and we've said to the lads come back stronger and make sure we get in the play-offs next season."
Harriers needed to beat Mansfield to give themselves a chance of reaching the play-offs and the game was evenly-poised until Lee Vaughan was shown a straight red card for an elbow on striker Matt Rhead at the start of the second half.
Mansfield were ruthless to take advantage, with Lee Stevenson, Louis Briscoe and Matt Green on target.
However, by the end of the game fans, players and management were more concerned for striker Anthony Malbon.
The young striker had been floored by Louis Briscoe's reckless shoulder barge and needed nine minutes of treatment by physio Gavin Crowe for a blow to the head.
However, an air ambulance landed on the Aggborough pitch to take Malbon to the Queen Elizabeth Hospital in Birmingham.
After being scanned and assessed by doctors in Birmingham, Malbon was given the all-clear.
Whild said: "I must say that Anthony has had the best possible treatment available and the signs are he'll be okay, so we'll keep our fingers crossed and the club wishes him all the best.
"I didn't see the [Vaughan] incident but it was a straight red card, so the referee saw something and it's always difficult when you're trying to win the game with 10 men."
Whild also felt Harriers' plight was not helped by an over-sensitive referee.
He added: "In a game where the two teams weren't trying to committ too many fouls the referee made hard work of it I thought.
"If he's missed something there I am not surprised because I don't think he had a particularly good game."
"That's not taking anything back from Mansfield, from our point of view he didn't influence the result.
"We're not looking to blame the referee. I didn't see the Malbon incident the but lad has taken a hell of a whack, so there is something that did happen but let's hope Anthony is okay and he recovers."