The Daniels dominated large parts of the Evo-Stik League Division One East clash, but paid the price for squandering a host of good chances.
Grant Ryan also saw a first half penalty saved as Stamford suffered their second home league reversal of the season to slip down to 10th place in the table.
Manager Graham Drury said: "We had 72 per cent possession and eight chances to their two, but they're got a 100 per cent conversion rate with their chances in front of goal and we're at zero.
"There is no more really to add to that. You can't miss gilt-edged chances like we have.
"Confidence comes from within in front of goal and I've tried to say to the players that we're the third top goalscorers in the division, we've scored nine goals in the Lincs Cup and four goals in two games in the FA Cup.
"But we're missing chances so everyone is asking where's the strikers and I'm asking the questions myself.
"I'm trying to re-address it. I've got seven days in for the lad who has got two goals against us.
"He's gets teams up the pitch, he gets hold of it and he's awkward.
"He sticks it away when he gets the chances. He's scored the penalty, we've missed ours. He's got a chance when through on goal, we've missed ours, but he's stuck his away.
"He gets goals, he's scoring goals and he's full of confidence and I'm afraid that's what we need.
"That's been the difference in this game. It's the bottom line which has perhaps been questioning us for maybe a year.
"I thought passing-wise, possession-wise and the movement was good. I've got no arguments with the way we played.
"The tempo could have been a little bit quicker because it was a bit like a training game at times with the possession we had.
"But they've come here to do a job and, to be fair, they've come away with all three points by creating two chances and taking them."
Stamford made just one change to their starting line-up from Tuesday's FA Trophy replay win over Belper with Reece Morris coming in for Ollie Brown-Hill.
The Daniels started the half on the front foot with early efforts from Grant Ryan and Reece Morris narrowly failing to break the deadlock.
They were then awarded a penalty after 16 minutes when Bradley Fortnam-Tomlinson was hauled down by Riece Bertram after latching onto an astute flick from Jordon Cooke.
However, Carlton custodian Jack Steggles plunged low to his right to tip Ryan's spot kick onto the post and deny the striker his third goal in four games.
Carlton came more into a stop-start contest as the half wore on with Opoku going close on a couple of occasions as the opening period finished goalless.
Stamford brought on Brown-Hill at half-time for Morris and he headed a Kern Miller cross into the side-netting while Ryan rattled the crossbar from close range with a header from a Joe Burgess centre.
Ryan was then thwarted by a super stop from Steggles who showed superb reactions to block his fierce close range strike.
Miller then headed wide when well placed from a Jake Duffy corner before Fortnam-Tomlinson fired another good opening wide after latching onto the ball in space.
The deadlock was then broken with 15 minutes remaining when Chris Salt was adjudged to have handled a cross into the box and Opoku converted the resultant spot kick.
Stamford continued to create chances with Steggles thwarting Fortnam-Tomlinson after he broke clear in the box following a Brown-Hill through ball.
Miller was pushed up front as Stamford launched a series of late raids, but the finishing touch was elusive and Opoku sealed Carlton's success in the final minute when he latched onto a long clearance and powered clear before sliding his effort past the advancing Dan Haystead.