Nottingham Forest were given a 'free goal' but lost their replayed Carling Cup tie with Leicester 3-2.
Clarke is on loan at Leicester from Premier League side Sunderland
The original second-round game between the two sides was abandoned with Forest leading 1-0 at half-time after City's Clive Clarke suffered heart failure.
Sportingly, City allowed Forest keeper Paul Smith to score straight from the kick-off to replicate the scoreline.
And City chairman Milan Mandaric said: "This will not hurt football, I'm proud of the players and happy we did it."
He added: "The idea came from the whole club - we all like to win games but morality and fairness is also important.
"It was a difficult situation, but it was the right thing to do."
Leicester boss Gary Megson said: "I had a chat with Forest manager Colin Calderwood 20 minutes before the kick-off to explain what we had in mind but it was kept very quiet until just before the start."
Calderwood added: "Leicester felt it was the correct thing to do and I must admit it took us back a little bit to start with.
"But it was an honourable gesture and I would like to think that football in general has come out of the game as the winner.
"I think the crowd took it in the spirit it was intended."
Football League chairman Lord Mawhinney has also commended Leicester on their act of sportsmanship.
The sporting attitudes shown by Nottingham Forest and Leicester City across these two matches reflect extremely well on the game of football
Football League's John Nagle
"Leicester's actions are a demonstration of football at its very best," added Football League head of communications John Nagle.
"Lord Mawhinney had also contacted Nottingham Forest following the original match to congratulate them on their good sportsmanship in agreeing to the abandonment of the game.
"The sporting attitudes shown by Nottingham Forest and Leicester City across these two matches reflect extremely well on the game of football."