Reigning champions England fully deserved their win at the Beroe Stadium in Stara Zagora.
They duly topped Group D, advancing to the quarter-finals along with Italy, who secured the draw they needed against Holland in Bourgas.
Despite their dogged efforts, Ireland propped up the pool with just one point and, most disappointingly of all, no goals.
Edwards' 71st-minute strike was worthy of winning any match. Skilfully making room on the edge of the area, the Tottenham striker sent a rising shot past Caoimhin Kelleher and into the roof of the net.
"It was disappointing as we had some very good chances," said Ireland boss Mohan. "We needed that first goal against such good quality opposition. The attacking players England have are fantastic.
"At the same time, it's been the story of our campaign that, when we did create chances, we just weren't clinical enough."
As their 13 attempts to one emphasised, England had much the better of the first half.
The best of those England chances fell to Ike Ugbo, whose shot was bravely blocked by Darragh Leahy, Ireland's most impressive defender this week.
Kelleher then made the save of the game with a fine one-handed stop from Nathan Holland's drive on 34 minutes.
Ireland's one chance came when Connor Ronan hounded Jay Dasilva off the ball to set up Josh Barrett, who drilled wide.
Ireland showed far more purpose on the resumption, blowing their best chance of the game three minutes in.
England keeper Paul Woolston could only parry sub Anthony Scully's fierce drive. JJ Lunney looked set to score from the rebound, but his weak lob was hooked clear by Danny Collinge.
Another bright opening for Ireland on 62 minutes saw Barrett set up Zackary Ebouzedi who fired his shot wide.
"I'd say they were the best of the three teams we played," said Mohan on England.
"Our boys gave everything they had and you couldn't ask anything more.
"We've been competitive in every game and we played some brilliant football along the way."
Republic of Ireland - Kelleher (Ringmahon Rangers); O'Keeffe (Birmingham), Masterson (Liverpool), Leahy (Coventry), McCourt (West Brom); Agyei-Tabi (Arsenal), Livingston (Wolves); Wade-Slater (St. Kevin's), Ronan (Wolves), Lunney (Preston); Barrett (Reading). Subs: Scully (West Ham) for Wade-Slater (34), Ebouzedi (West Brom) for Livingston (58), Aherne (Lucan United) for Barrett (75).
England - Woolston; Yates, Oxford, Collinge (Sulliman, 49), Dasilva; Wright, Kane; Holland, Edwards, Ndukwu (Willock, h/t); Ugbo (Mavididi, 72).
Ref - P Raczkowski (Poland)