Interim manager Curtis closed his reign in charge of team affairs with a 1-0 victory over Watford, which takes Swansea above Newcastle and out of the Barclays Premier League relegation zone.
Curtis will remain part of the Swansea set-up but Guidolin's appointment as head coach was confirmed before kick-off and the former Udinese boss had a watching brief from the stand as the Welsh club recorded only their third win in 18 league games.
"I've always said I was quite happy (to step aside) if the club thought it was necessary to bring someone in," Curtis said after securing a second victory in seven league attempts after succeeding Garry Monk in December
"If we had won more games, then possibly, that might not have been needed.
"I think the performances have been excellent but we haven't had the results those performances warranted.
"We could have been four, five, six, or even seven points, further on.
"But by bringing in an experienced coach we can turn those performances into points.
"Sometimes you maybe need that managerial experience at the top level to get the points that go with the performances."
Curtis said club chairman Huw Jenkins had told him about Guidolin's arrival after the players had trained on Sunday, and that he has yet to meet the Italian in person.
Guidolin, 60, has brought in former Chelsea midfielder Gabriele Ambrosetti to assist him and Curtis said it was a set-up capable of saving Swansea from the drop.
"You can't have a joint managership - it's got to be one or other and I'm quite happy for Francesco to have that," Curtis said.
"I will have far better knowledge of these players than Francesco and I'm readily available to pass on that information.
"But my concentration was on the game tonight and the win was massive.
"We talked about the need to pick up three points.
"I thought in the first half we were excellent and over the course of the 90 minutes we deserved it.
"We got a bit edgy in the second half but that's more because of the situation we find ourselves in."
Watford have now suffered four straight league defeats and failed to win in five games.
The Hornets only came to life in the second half but were unable to cancel out Ashley Williams' 27th-minute header.
"I think we are not happy with the first half," said manager Quique Sanchez Flores.
"In the second half, we were good
We played football, but we need to accept the result.
"This is football
You never know when you will win lose or draw.
"This is the Premier League
We have just come up
We have lots reasons to be happy.
"When we had four wins in a row we were humble.
"I don't like to lose but we need to accept the results - and we have enough points to be positive."
Source : PA
Source: PA