A stunning goal from Fleetwood full-back Conor McLaughlin with 20 minutes left sealed the Cod Army a 2-1 win and a place in the Northern Area final after Rotherham's on-loan Wigan striker Nouha Dicko had cancelled out Jeff Hughes' first-half opener .
The two managers clashed on the final whistle, with Evans insisting Fleetwood had not deserved to progress at the expense of his side.
He said: "We've gone out so it's extremely disappointing.
"But the second-half performance was emphatic. It shows we're a county mile ahead of Fleetwood.
"But you can't allow for two goalkeeping errors and a load of missed chances.
"I've said to the players, people will look at the result but not know the circumstances."
Hughes had put Fleet ahead after 19 minutes. Nathan Tyson's persistence paid off as he tumbled in the box and Hughes scuffed his shot through the legs of Adam Collin.
The Millers dominated the first half, but grim determination kept them at bay..
The dam finally broke 10 minutes after the break. Kieran Agard had already hit a post and on his next foray forward the striker's shot was blocked by Mark Roberts and Dicko followed up at the back post to fire home the equaliser.
McLaughlin then hit the winner before there was late drama as first Rotherham midfielder Lee Frecklington and then on-loan Newcastle defender James Tavernier forced added-time saves from home goalkeeper Scott Davies as Fleetwood held on.