Despite dominating for most of the second half, Mike Dove's side were made to pay for their slow start by a clinical Bulls side who will now go on to face either Chester or Chesterfield in the next round.
The Young Dons made a slow start to proceedings and they were given a brief scare in the ninth minute when Bulls striker Dylan Bonella skimmed the crossbar with a glancing header.
England Under-18 international Brendan Galloway then had a half-chance to break the deadlock following a surging run forward before the Bulls took a surprise lead on 20 minutes.
After winning a free-kick out on the left flank, Hereford’s Cory Williams was able to pick out Max Kontic-Coveney with his cross and the defender turned the ball past Dons ‘keeper Ben Taylor to give the Skrill Premier side the lead.
Coveney’s goal seemed to unsettle the Young Dons, who struggled to get their free-flowing football going in the first half, and on 30 minutes they fell further behind when Ben Miller beat Galloway to Max Brock’s cross to finish well at the near post.
Despite being two goals down, the Young Dons refused to let their heads drop and they could have found a way back into the game three minutes before the break had Giorgio Rasulo’s clever pass been a little easier for Will Summerfield to control inside the Hereford box.
Ben Tilney also went close to reducing the deficit late in the first half, but his fierce long-range effort could only sting the palms of Evans.
With Dove’s half-time words no doubt still ringing in the players’ ears, the Dons began the second period brightly and Weston came within an inch of opening his account for the season with a volley straight from the re-start.
Kabongo Tshimanga then spurned a glorious opportunity to make it 2-1 on 54 minutes when he placed a shot wide of Evans’ goal before Kelvin Osei-Addo struck the underside of the bar with a terrific effort on the edge of the box.
However, despite spending most of the half camped inside their own half, Hereford secured the victory with 13 minutes left to play; Billy Murphy climbing highest inside the Dons box to head powerfully past Taylor.
Galloway did go close to a consolation late-on with a tight-angled effort which bounced off the crossbar but it just wasn't to be for the Young Dons, who had to travel back to stadiummk without a goal to their name.
MK Dons (4-2-1-3): Taylor; Grant (Collinge 46), Hickford, Galloway, Tilney; Wiltshire, Weston; Summerfield; Tshimanga (Tingey 84), Rasulo, Osei-Addo.
Subs: Van Der Schoot (GK), Daffern, Vaughan.