Swansea boss Michael Laudrup admitted Arsenal deserved their 1-0 FA Cup third round replay victory.
Jack Wilshere scored a superb winner for Arsenal with four minutes left of normal time, and it was no more than the hosts deserved.
Swansea had set up the replay with a late Danny Graham goal in the 2-2 draw and Laudrup had no complaints to be denied by a similarly late goal at the Emirates.
Laudrup said: "The first half was very even, they had a bit more of the ball but we were at the same level.
"In the second half they were the better team, they deserved the win and good luck in the competition.
"They created chances and pushed us back, we defended great but we couldn't get out of there.
"It was nice to see Michel Vorm back at his best and we blocked a couple of big chances.
"They had one or two where you say 'How did they miss that?', and then they scored with a few minutes left.
"Last time it was us, this time it was them."
The Sky Blues were in complete control in the first half and the only disappointment for manager Mark Robins was the fact they only had one goal to show for their dominance.
Gary McSheffrey shot wide after a strong run in the fifth minute before full-back Cyrus Christie forced Owain Fon Williams into a smart stop shortly afterwards after cutting in from the right.
The home side took the lead in the 19th minute when Carl Baker floated a corner to the back post which Richard Wood headed straight into the path of a grateful Clarke and he volleyed home from close range.
Clarke should have doubled City's lead nine minutes before the break but he headed straight at Fon Williams from Baker's cross.
Tranmere could only improve in the second half - and they did - but it was still Coventry who were on top and McSheffrey went close on three occasions.
The closest Ronnie Moore's team came to an equaliser was a goalmouth scramble in the 71st minute which began with an Ash Taylor header being saved, but the home side eventually cleared.
Joe Murphy made a fine save in the dying minutes to deny Zoumana Bakayogo.