The defender says a lot of unlucky things happened to the Toffees on Sunday and believes his side did not play badly.
Anthony Martial scored the only goal of the game as Roberto Martinez's side suffered a third consecutive loss in a further blow to their hopes of securing a top-flight finish.
Although the Toffees were far from impressive in attack, they defended relatively resolutely until a deflected cross fell nicely for Martial to convert nine minutes after half-time.
Even then, Everton could have salvaged a point had Phil Jagielka's header been an inch or two lower instead of crashing off the crossbar, or if Stones' defensive partner had been able to beat David De Gea late on.
The defeat has only served to increase the scrutiny on the Merseyside club and manager Martinez, but Stones was defiant in his assessment of the performance and result.
The 21-year-old told the club's official website: "There were a lot of unlucky things that happened to us today, the goal was one of them. Before that, I didn’t think they had a spell in the game where they looked like they were going to score. We hit the bar and had chances to win the game but the things that are going wrong are costing us.
"You’ve got to take some positives. Defensively, I thought we looked strong, except for the goal which crept in at the back post. Going forward we should be confident that we can bring this [defensive] performance to the table week in week out, then go out to express ourselves and score goals.
"Some things you can’t put right, like luck, but the things we can control we need to work on in training. We have got the players and have got the work-rate. We’ve showed it this season that we can do it, so we need to look in the right direction."
The latest defeat leaves Martinez's side 12th in the league table, six points off even a place in the top half after another underwhelming campaign.
Despite Stones' staunch comments, Toffees captain Jagielka admitted after the match at Old Trafford that he does not now what the solution is to the club's recent poor form.
However, the three consecutive losses that the club has now suffered in the league since beating bottom side Aston Villa on 1 March have all been to clubs currently in the top six, in the form of West Ham United, Arsenal, and the Red Devils.
Everton must now refocus on a hectic league schedule over the next few weeks before their FA Cup semi-final at Wembley, where they will either face a rematch against United or a clash with West Ham, depending on the winner of the quarter-final replay at Upton Park.