Young defender George Cooper was adjudged to have fouled Portuguese star Youseff Chermiti in added time at the end of an entertaining game and Chermiti buried the spot kick.
After exits in both the Carabao Cup and FA Cup this week, tonight's result was the least of Stags' concerns as they played largely a second string ahead of Saturday's big league trip to Salford City.
But Clough said: “We didn't want to lose the game - and we didn't deserve to lose in the manner we did.
“For the referee to give that penalty, I am not surprised there are so many people in football commenting and saying the things they are when you see it at this level tonight in this sort of game, which you see it decided on a decision like that.
“But I am not too disappointed with the cup performances, despite losing the games.
“We have lost three games by the odd goal here this week but all could easily have been different results.
“We haven't done much wrong in the games and we have kept our standards and consistency high – and that is what we're going to need in the next five months.”
Clough made nine changes and said: “A lot of lads needed the minutes tonight and it was a good 90 minutes for the likes of Will Swan and James Gale.
“George Cooper got 90 minutes and was very good, George Williams had been ill at the weekend but got through 90 minutes, though was struggling by the end. Everybody got what they needed.”
Everton played a strong side and Clough said: “You could see the speed of them on the break.
“They had some Premier League squad players out there and you could see the difference – the athleticism and the pace.
“The lad who came on on the right hand side was absolutely catching pigeons out there.
“Scott Flinders made two very good saves, especially the one going to his right when he stuck his left hand out. Competition is good with our keepers and it was good for him to keep his hand in tonight.
“I was pleased with everybody tonight. It's all about the attitude and work rate and I thought they were spot on tonight.”
There was a worry for Stags when Stephen McLaughlin had to come off just after half-time after impressing on his first start after injury.
“Stephen McLaughlin just felt his groin tonight. I am not sure how bad it is but it was precautionary bringing him straight off,” said Clough.
There was no place tonight for strikr Rhys Oates, also coming back from injury, who impressed and scored against Wrexham on Saturday.
“Rhys was not involved against Everton but did enough on Saturday so needed the breather tonight looking towards the weekend,” said the Stags boss.