While he received treatment, Leicester added to the pain by equalising through Martyn Waghorn - and the 25-year-old now faces an anxious wait to see if he will be fit for the potentially crucial Northern Ireland World Cup qualifier against the Czech Republic on October 14.
Manager Chris Coleman said: "Sammy was caught late and was off the pitch when we conceded but what can we do?
"We don't know how bad the injury is yet - we need to see it when the swelling goes down, but it's quite badly bruised.
"We're disappointed because we wanted to the win the game and the one time we've knocked off defensively from the second phase we've been punished.
"You know what derby games are like -all form goes out the window - but it was a good game.
"We didn't get the three points but we were against a tough team and I was happy with the response from the players."
Coventry started brightly and Aron Gunnarsson had two chances in two minutes to open the scoring. First, he sent a powerful shot just over the bar from 18 yards.
Then, he sent a shot towards goal inside the penalty area, but Leicester keeper Chris Weale blocked well.
Leicester threatened through Paul Gallagher and he rattled the crossbar in the 23rd minute with a long range effort.
Gallagher was involved in the opening goal 15 minutes later - but not how he would have liked. The Scot handled the ball on the corner of the area, and Clingan sent the ball into the top corner for his third goal of the season.
Nigel Pearson had seen enough by the 60th minute and made three substitutions.
The gamble worked 10 minutes later when two of the replacements - Steve Howard and Waghorn - combined to level. Howard rose well to head the ball into Waghorn's path, and the striker coolly knocked the ball past Westwood on the half-volley.
Pearson said: "I don't know about management genius but it was a gamble worth taking. We have a strong bench and we really did feel that we could win the game.
"It made the game more open because they had chances but it worked. Martyn's finish was fantastic. He is a young player who will only gain from his experience of coming to us.
"I thought it was an enjoyable encounter because both sides were trying to win it and had a good go, but I felt that we were the better side."