"The fans were fantastic (in Saturday's 3-0 win at Lincoln), but sometimes they can give a bit of stick, certainly to me personally," he told BBC Sport.
"But I'm there to score goals and if you get me fit that's what I'll do.
"The supporters are the 12th man out there, and that's what we need. The fans have to play a part, and if they believe in us we'll do it."
McEvilly, who has come under criticism from certain sections of the Wrexham fan base for his work rate, got the final goal in the Lincoln win as the Dragons raised themselves out of the League Two relegation zone.
Wrexham manager Brian Carey was delighted after the win, and seemed to contradict McEvilly's opinion on the Dragons' support.
"The fans kept the faith and belief after last week's home defeat to Notts County and that's boosted us all, they've been terrific," Carey told BBC Sport Wales.
"You can't ask for any more than the players delivered at Lincoln, there were 11 players who performed without fear and just went for it.
"There were so many positives, and we just have to maintain those for the next four games.
"The relegation situation is going to chop and change, but right now we're out of it so let's keep it that way."
McEvilly was keen to praise Carey's role in building Wrexham's confidence.
"Brian told us to leave the Notts County result behind, not to dwell on it and to think positively," said the Northern Ireland international striker.
"The disappointment was out of us by Monday and we trained hard all week.
"Then we came to Lincoln - one of the top sides in the league - and gave our best performance of the season, we dominated and bullied all over the pitch."
BBC