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The Italian's reign began with a much-needed 2-1 win at Goodison Park.
Swansea are up to 15th in the Premier League table and are four points clear of the relegation zone after a second successive win.
"Confidence is very key and our confidence is improved," Guidolin said.
"The table was not good and still not good. Day-by-day we will play more matches and try to win."
Gylfi Sigurdsson's penalty gave Swansea the lead but Everton levelled when Gareth Barry's near-post flick from a corner was touched into his own net by Jack Cork.
Andre Ayew's deflected strike secured Swansea's first ever league win over Everton and back-to-back victories for the first time this season.
Former Udinese and Monaco coach Guidolin had watched Swansea's 1-0 win over Watford on Monday from the Liberty Stadium directors' box.
"It's all new and my first Premier League game was away against a very strong team like Everton so it's fantastic [to get the win]," Guidolin added.
"This is a new world but football is the same."
New head coach Francesco Guidolin says Swansea's victory at Everton will give them confidence in their bid to stay in the Premier League.