The in-form Clarets brushed the Stones aside 3-0 on Monday night, all but ending their faint play-off hopes.
Their form hasn’t recovered since the FA Trophy semi-final defeat to Brackley Town and Wilkinson is demanding more.
The Stones travel to rivals Hemel Hempstead on Thursday and their boss has demanded his side don’t end the season with a whimper.
“One team was on the beach and one was fighting for their lives and that was clear to see,” Wilkinson admitted after the Chelmsford defeat.
“They outmuscled us in the first half. In the second half we huffed and puffed but it wasn't good enough. You’ve got to wear the badge with pride and I told the lads that at half-time.
“Our boys are running the clock down now game by game and it’s only going to get harder. They need to have some pride, passion, guts and determination.
“We’ve got a local derby (at Hemel Hempstead) on Thursday. Will the lads go out with a whimper or show some fight? I’ll wake up in the morning and be fighting to get this side showing some passion again.”
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