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The club's American owners have become concerned with the Swans just one point clear of the relegation zone.
But Guidolin has not met chairman Huw Jenkins to discuss his future and insists he is not under pressure.
"I don't know what the owners and chairman are thinking - for me, it is not important," he said.
"Instead it is important to work with my players and have a good relationship with them.  Today they gave a good performance.
"I have not spoken to the chairman. I do not feel under pressure. It's my job. I do not need to speak to him. If the chairman has to tell me something it is the easiest thing to do.
"In this period our fixtures are not easy. We are not in a good moment for results. But today I saw my team grow up."
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Swansea 's American owners, Jason Levien and Steve Kaplan, and Jenkins have been alarmed by Swansea's recent poor form.
With difficult fixtures against Liverpool and Arsenal to come, however, it is understood the quality of Swansea's next few performances will have as much bearing on Guidolin's future as the results.
Having been distinctly unimpressive in last Sunday's defeat at Southampton, there was a marked improvement in Saturday's encounter with Premier League leaders City.
"The performance was perfect in my opinion, the same level of Manchester City who are the best team in the Premier League," Guidolin added.
"I am proud of my players. I am disappointed by the result but this our job.
"Before the penalty we had the chance to score and we deserved to score. It was a good game and now there is disappointment in my team and me but, if we play like this in the future, then the future will be good for us."
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Francesco Guidolin believes his Swansea City side are improving despite suffering a fourth loss from six Premier League games with Saturday's defeat by Manchester City.