Curtis picked up his first point since being put in temporary charge following the sacking of Garry Monk as Swansea fought out a goalless draw with West Ham at the Liberty Stadium on Sunday.
The draw was not enough to take Swansea out of the Barclays Premier League relegation zone but, just like Curtis' dug-out debut in the 2-1 defeat at Manchester City last weekend, it was an improved performance compared to the final games of Monk's 22-month reign.
Swansea chairman Huw Jenkins hopes to name a new manager in the next week - with former Argentina and Chile coach Marcelo Bielsa still the preferred choice - but Curtis says his job is to focus on preparing the team for the Boxing Day visit of West Brom and the trip to Crystal Palace two days later.
"We are preparing as if we are in charge, there is a quick turnaround of games," Curtis said after Swansea had ended a run of three successive defeats.
"We have to prepare not just for West Brom, but for Palace.
"If someone comes in they can take the reins but we have to prepare.
"It is important to bring someone in sooner rather than later, but it is more important to get the right man.
"If that takes a while then we are happy to carry on - and we assume we will be in charge."
Swansea dominated for long periods but they struggled to create chances and break down a resilient West Ham defence.
But Curtis felt they should have been awarded a 62nd-minute penalty when Ki Sung-yueng's goalbound shot struck the hand of Hammers defender James Collins.
"I was not sure at the time, but when I see it again it looks like a penalty," Curtis said.
"Down the bottom you do not get the decisions you deserve.
"We just need that good fortune and we are frustrated.
"In terms of possession we were excellent, we looked like Swansea City again.
"We bossed the game but we just lacked that killer edge up front."
West Ham have now gone seven games without a win since beating Chelsea at the end of October to go third in the table.
Injuries to Dimitri Payet, Diafra Sakho and Manuel Lanzini have blunted their attacking edge and Andy Carroll was also absent at Swansea after suffering a midweek groin injury.
"We created more than enough chances to score at Old Trafford a couple of weeks ago, last week at Stoke we had the most shots in the round of fixtures and here we had a few situations," West Ham manager Slaven Bilic said.
"But the quality in the last third is a big question mark, although I praise the players for their performance.
"We were very resilient and stubborn in a positive way, we defended very well and I thought we deserved a point.
"We were really hit with injuries four or five weeks ago, especially up front, and I said the only way we were going to compensate was with the team performances in these games.
"It's a very good cornerstone what we have done and when these players come back in the next week or two it makes us very positive."
On the penalty incident surrounding the Collins handball, Bilic added: "He tried to make a block on a shot that was 100 miles per hour
"So I would have to guess or lie to say something on that
I don't know."
Source : PA
Source: PA