The pride in his players' performance was tempered by frustration at the referee who, Morgan believes, cost Halifax the game.
His side had battled back brilliantly from a 12-0 interval deficit to lead 17-12 with 10 minutes to go.
But they allowed the hosts in for an unconverted try to level things and with the clock ticking down the referee awarded Blackheath a penalty in front of the Halifax posts and full back Frankie Neale stole the points with the kick.
"It was a heartbreaking way to finish a game and I just feel so sorry for the lads," said Morgan.
"We were clapped off the pitch by the Blackheath people because they knew we should have won that game.
"But at the end of the day it is still difficult to stomach the fact that we have lost and I believe the referee played his part in that."
A clearly frustrated Morgan did make his feelings known to the official immediately after the final whistle and called on him to look at the match video, although he accepted it wouldn't change the outcome.
"Unfortunately the man in the middle had the ultimate say and he decided that it wasn't going to be our day," said Morgan.
"To my mind, he needs to have a look at the video. Blackheath constantly held on to the ball on the floor, they constantly came in from the side and the referee never saw it all afternoon.
"The minute he saw anything on our side it was a yellow card and I had a key man sitting beside me for 10 minutes in which time Blackheath scored their first try.
"I am not happy because it is my opinion that he cost us the game."
One thing Morgan could not dispute was the attitude and application showed by his players who were tremendous all afternoon.
They overcame injuries to key personnel to battle back in the second half and open up a 17-12 lead following tries from Matt Harrison and Joe Knowles, who also utilised his trusty boot to good effect.
But it was a solid defensive effort during a tough first half that really kept Halifax interested.
"I am just so pleased that we can show what we can do when we have a relatively strong side out and that includes all 19 players," added Morgan.
"We had to make changes because we lost George Jenkins, Benny Mitchell, Will Kay and Gareth Lewis, for a while, but we still got stuck in and worked hard and every credit to the players.
"Once we get over the scoreline we can see there were so many positives to take from that game. We deserve a pat on the back. It was a moral victory and the players knew they could go into the Blackheath clubhouse with their heads held high.
"It is a shame that we have to bow out of this league but we are not going to bow out without a fight.
"We deserved a win and let's hope we can pick one up over the next two weeks.
"We have Waterloo at home and Wharfedale away and if we can work as hard as we have against Blackheath then who knows?"