United, who entertain Port Vale at Bramall Lane this afternoon, are ninth in League One and trail sixth-placed Millwall by five points, with 15 games of an inconsistent campaign remaining.
But McEveley said: “We’ve got to say, ‘we can do this’. Believe we can do it and then hope the people who come to see us cheer us on.
“When I first went to Derby, we were second I think and a few points off the top. The rest of the season didn’t go as we would have wanted and, with a few games to go, we realised we couldn’t make the top two. We ended up in the play-offs and there was a lot of disappointment.
“But we all got together and realised; we were good players and had to push on. We got promoted through the play-offs. We’ve got to look at it like that now.
“We all got together back then, fans included, staff and everybody else and got through it. There was light at the end of the tunnel when it all seemed like gloom and doom.”
United were again heavily criticised by their travelling supporters after Tuesday evening’s disappointing defeat at Bury, which saw them miss the chance to close the gap on the play-offs.
“Supporters are entitled to their opinion. They pay to watch games and at certain times they’ve not been happy with them,” McEveley added.
“We accept that and we take it on our shoulders. There’s personal pride too. When you are playing for a club of this size, you don’t want to let all those people down.
“That’s what happens, that’s the expectation at a club of this size and we have to deal with it.”
“Our consistency levels have not been good this season,” McEveley added.
“There’s no hiding from that. I think it’s a mental thing a lot of the time; it does play on your mind when things aren’t going well.
“Of course, it affects you. But we’re professionals and we have to get over that.
“We can do all the talking we want in press conference or in the dressing room. But it’s when we step over that white line, that’s when we are judged.”