“We brought Alberto in to score goals but the responsibility has to lie with the team,” said Curtis.
“Alberto wasn’t brought in to be the main man but to make a contribution.
“I think we’re too reliant on Andre and Gylfi to get our goals, and it needs to be spread out.”
Swansea visit second-placed Tottenham on Sunday, taking on a team second in the Premier League scoring charts with 47 and who have conceded only 20, fewer than any other side in the division.
By contrast, the Swans hover just three points above the relegation zone in 16th place.
Spurs face Fiorentina in the second leg of their Europa League tie on Thursday and are just two points behind the Premier League’s surprising leaders, Leicester, with 12 games left in the league season.
“I think they’ve [Tottenham] done exceptionally well,” said Curtis.
“They’ve got a great opportunity to win the league this year and they’re still in the Europa League.
“I don’t see any reason why they can’t [win the league]. They’ve shown this year they can go all the way.”
Montero’s demise mirrors Swansea’s
Swansea have a fully-fit squad for their trip to White Hart Lane, and there could be scope for changes following a 1-0 home defeat to Southampton in their last outing.
Winger Jefferson Montero is among the players hoping for a recall, having drastically fallen out of favour.
After a sparkling start to the season, the Ecuadorian has not started a league game since December and was left out of the match-day squad to face Southampton, he has featured only once in the Premier League this year.
“Jeff’s form mirrors the form of us as a first team,” said Curtis.
“He started the season really well and just started falling away for whatever reason.
“I think certainly Jeff has suffered from us switching to this diamond system.
“He’s an out-and-out winger and I think, because of that, he hasn’t had the game-time.”
Asked if Montero and other players to have lost their places, such as striker Bafetimbi Gomis, could force themselves back into first-team contention, Curtis said: “Absolutely.”
“For Jeff and Bafetimbi, the opportunity will always be there for them.”
Tottenham will be without midfielder Mousa Dembele (groin strain) for Sunday’s clash, meaning former Liberty Stadium loanee Tom Carroll, who played 20 games for Swansea in 2014/15, is likely to start against his former club.