The Liverpool-born defender was part of the Swindon side who somehow managed to become one of just a handful of League One teams who got the better of the Blades during a compelling final three months of last season – and still is not sure how.
The date was March 29 last year when McEveley was part of a Robins line-up who faced a powerhouse Blades side who had won 12 out their previous 14 fixtures and fortuitously beat them 2-1 thanks to a late goal from Louis Thompson.
Yet McEveley remembers it not for the victory, which inflicted a hammer blow on the visitors’ thrilling pitch for the top six, but the aura the Blades possessed and the feeling of awe among himself and his team-mates beforehand.
Ultimately, the Blades’ brave run for the play-offs and a return to the Championship after being in the relegation positions this time last year was too steep a climb, but the scale of the ascent is nowhere near as arduous this time around.
Automatic promotion is still on the vista and even accounting for the fact that Nigel Clough’s side do have considerable work to do from sixth spot, anything is possible if last season’s charge is anything to go by.
United fed off their sterling FA Cup exploits to energise their league form in the second half of 2013-14 and Sunday’s marvellous 3-0 cup win at QPR, allied to victory over a promotion contender in Preston today would help generate some significant momentum again.
Given last season’s events, if anyone is entitled to believe they can go on a season-defining run of games to gatecrash the top-two, it is the Blades.
McEveley said: “We are sixth in the league. I know some people might not think so, but that is good, especially when you think where the club was last season.
“We know what is expected of us and we expect it of ourselves.
“It is just a case of getting that run together, where you feel unbeatable every time you step on the pitch like the lads did last year. I think that is very close now.
“I remember last year, when I was at Swindon, we played United and although it wasn’t a feeling of fear, we knew what a mighty club they were and that they were on a real run.
“We won 2-1 but, in fairness, United deserved to win – I seem to remember Conor (Coady) missing a couple of chances. But that was the feeling in the Swindon dressing room then.
“If we can get on a roll then people will be coming to our place and thinking ‘whooah.’
“It is a lovely feeling as a player when you have that.”
He added: “When I went to Swindon from Barnsley (in March, 2012) under Paolo di Canio, we were second or third in the league and had that feeling, too, and ended up winning the League Two championship.
“We then went to League One and were sitting around the same position and then, by the end of January, we were top of the league and the momentum was going.
“Things didn’t pan out when Paolo left (in February, 2013) but it showed what can happen.
“It was the season Tranmere were out front and no-one thought they would be caught. But Bournemouth came steaming through with what felt like about 10 wins on the bounce and went up.
“Do not be surprised if that is the situation again because it always seems to happen in this division. It’s not too late, there is a lot of football to play.”
Alongside the Blades’ natural advantages in terms of fan power at League One level, several other factors should serve the club well in the definitive final third of the season, according to McEveley.
Squad strength, likely to be augmented by some new additions this month, being one, alongside a fitness ethic born from doing some punitive hard yards in pre-season with many players also somewhat seasoned to graft by virtue to the club’s 57-game campaign last term.
McEveley said: “We are confident because of the performances, there are no gripes there.
“It is just coming down to putting the ball in the back of the net a little bit more and stopping sloppy goals. We are not killing teams off when we are on top.
“But the way the gaffer works, especially with emphasis on fitness, I think we will really come on strong in the second half of the season.
“Teams with lesser squads will start to dwindle but we can kick on with the size of the squad and the conditioning of the lads here.
“What we want to do is keep ourselves up there, push on a bit and then kick on in the last 15 or so games. Leagues are not won in December or January.”
McEveley’s durability so far this season has been noteworthy, having vacated the left-back berth he has occupied for most of his career to move into the centre.
It is a role which sits well on a player who turns 30 next month, with his sense of ease on and off the pitch bringing out the best in a player who, like a fine wine, is maturing with age.
He continued: “I am loving it here and am really enjoying it. I loved it at Swindon. But I was living away from home with my missus and kids back in Liverpool.
“Now I am settled and drive through with Higgy (Michael Higdon) and stay over a few times a week, so we are not doing the drive all the time. I feel much happier in myself.
“I also think it has helped that the manager has changed my position.
“I am really enjoying myself at centre-half and, at my age, I think it suits me because I am no Ashley Cole and can’t play left-back forever.
“People always said that’s where I would end up although it has come a little bit earlier than expected.
“If someone asked me now what I am, I would say a centre-half.”