The former England international also believed it was wrong for a player as young as 19-year-old Bukayo Saka to take the decisive final spot kick.
“It was heart-breaking,” said Clough. “I just think Italy had a bit more experience and probably deserved it on the day. That was always the thing - England are a young squad.
“But I hate penalties. I get it that you've got to decide a game and I honestly don't mind it in the group stages and the quarter and semi-finals.
“But in the final just keep playing. Play until you drop. I don't care. It's the final.
“You are not preparing for another game. It doesn't matter if you are tired. You win as a team and you lose as a team.
“It might force an individual mistake but there is 11 of you on the pitch. Don't let a final be decided on one person's shoulders.
“That's wrong. That's not the spirit of football.”
He added: “The only other thing I would say is should a 19-year-old be taking the fifth penalty.
“Experienced players should be in that position. He shouldn't carry that weight at 19 years old.
“Three or four days earlier we saw what happened with the young girl at Wimbledon. She is only young and it's just too much to put on a youngster's shoulders.
“He was carrying 55 years of expectation for that one penalty.
“Other than that is was all positive.”
Overall, he said: “It was almost the good the bad and the ugly over the tournament.
“I think what Gareth Southgate did with the team, especially getting to the final, was absolutely brilliant. And it was the manner in which they did it as well – the conduct of the players.
“It was the first major tournament that England have been in over recent times when there hasn't been anything negative coming out of the camp.
“I kept reading there were no egos in this squad – of course they have got their egos. But he persuaded them not to bring them to the England camp.
“He said 'leave your egos at the door if you're coming with us'.
“You set the tone with your captain and your senior players – Harry Kane, Harry McGuire, Jordan Henderson, Conor Coady, people like that. They set the tone.
“If the majority are decent lads the others will follow suit. I thought from that point of view they were fantastic.
“You can always pick holes in teams and selection – that is purely opinion – but I don't think the conduct of our players is up for debate at all.”
However the conduct of some fans who burst their way into the final for free, injuring people in the process was a different matter.
“It's just a shame about the scenes at the final,” he said.
“Again just a few spoil it for everybody else. Something has to be done as it's happening too often.
“They just ruin it for the vast majority of people who just want to go and enjoy what should have been the most important occasion for English football in 50-odd years.
“They need sorting out and it needs sorting out.”
Some fans believed Southgate should have been more adventurous, but Clough said: “I think first you have to be defensively solid, which they were – they only conceded a couple of goals.
“But I think there is a balance to be struck where we have such exciting young players that maybe you can let them off the leash a little bit more.
“I think that will come as the squad and this team evolve. I think that balance will improve.
“When you think from five years ago. He has now taken us to a semi-final and a final. I think there is a massive improvement there.”