Gylfi Sigurdsson's 81st-minute equaliser had looked as though it would extend their unbeaten run to three Premier League games, what would have been a first this season for the South Wales club.
But having already broke the deadlock on 11 minutes, City's January signing Gabriel Jesus reacted fastest late on to take advantage of Lukasz Fabianski's fumble and hand Pep Guardiola's charges a last-gasp 2-1 victory.
Despite losing so late on, the Swans boss believes his side deserved more at the Etihad Stadium and vented his frustrations at the circumstances surrounding City's late winning goal.
Swansea manager pleased with second-half improvement
Clement told his post-match press conference: "It was a very frustrating first-half. We were under a lot of pressure from the first minute right up until the 45th.
"To concede only one goal going into that period was, I think, a bonus to us. I think our shape defensively wasn't too bad but in terms of getting pressure on the ball and being aggressive in the one-v-one situations, it wasn't good enough.
"The few occasions where we did get the ball back, we were wasteful. It could've been a worse situation coming in at half-time but 1-0, there were lots of things to improve on and it was good that the half-time came because I needed to sort some things out.
"The players responded very well second-half, we were a totally different team. I thought we were the better team in the second-half - more confident with the ball, more aggressive defensively, scored a good goal.
"Clearly at the end you're very disappointed to have conceded in, I don't know what it was, ninety-two-and-a-half or ninety three minutes. It's a big blow."
'A draw would have been a fair result'
The 44-year-old, who ended a spell as assistant manager to Carlo Ancelotti at Bayern Munich to take over at Swansea at the start of January, took encouragement from how his side responded after half-time.
"That's the positive we have to bring away from the game," he continued when asked about their display after the restart. "We did enough over the 90 minutes to warrant a draw.
"I don't think we deserved to win the game, but a draw would have been a fair result. First-half like I say we were not good at all, but second-half I thought we were good.
"Every game that I've been involved in, we've tried to get the tactics right for the opposition that we're playing and to try and get a positive result. A positive result today would have been a draw based on the circumstances of the game.
"I understand that there's certain games that we're not expected to win. Maybe this wasn't one [we're expected to win]. But over the game, I would've expected a draw in the end."
Clement added: "I think after the first nine minutes, I looked up at the clock and I don't think we'd touched the ball.
"There were constant waves of attack and it didn't die down after that either. It was a very difficult first-half for me to watch that and for the players as well.
"But at half-time, we changed some things and it was much better in the second-half."
Clement 'disappointed' by free-kick for City winner
But Clement, who had overseen three wins in four league matches going into this tie, also expressed his disappointment with the manner of the second goal as he took exception to City's free-kick.
"In my opinion, it wasn't a foul," declared the Swans boss. "It was right in front of me. I thought [Luciano] Narsingh tried to evade the challenge of [Aleksandar] Kolarov and the referee or the linesman gave the decision thinking that he's got him and thrown him across the body and out of the way.
"That wasn't the case. Kolarov's gone to go shoulder to shoulder and he [Narsingh] has got out of the way of the challenge and Kolarov's gone across the front of him.
"But okay you can get those. It's the restart I'm disappointed about. It was 10 metres deeper than where the free-kick was, in a more central position. The ball's rolling and they're things the referee was picking up on all game.
"For example Martin Olsson, throw-in on the left, [the referee says] 'No go back to where you are'. Every time he got the ball, he tried to advance and he was pulled back into position.
"Fair enough, that's the rules. But that is a rolling ball taken 10 metres deeper than where it should have been and not even on the touchline, it was inside as well.
"The time that that ball takes to go back in its position and be taken in the correct place, I'm confident that my team are in a more organised state than it was when they took the free-kick.
"Yeah of course the ball's gone wide and it's crossed in and ultimately there's an error defensively right at the end, but I don't think it should have got to that point.
"I'm a little bit disappointed with the circumstances of the winning goal."