The Welsh outfit have not won a Premier League game since their opening-day victory over Burnley last month.
Guidolin's side were also knocked out of the EFL Cup in the third round by Manchester City.
There is no let up for the Swans as they face City again on Saturday in the Premier League, but Guidolin was encouraged by his team's performance in the Cup meeting.
"I am optimistic because I saw my players play a good game," Guidolin told reporters. "At Southampton, we deserved to lose, but in this game we started very well, with focus, aggression, intensity and good ball possession.
"We just have to look forward. If we play well and work hard, I think we are going to have some better moments. Saturday against Manchester City will be more difficult than [the EFL Cup tie]. They had a very good team, even if they played without some players, but on Saturday there will be new important players here."
Swansea are currently 15th in the Premier League table after picking up four points from five games.