The visitors had more than 70% of the possession at Villa Park but only came away with a draw.
Gabriel Agbonlahor exploited some poor defending to put the hosts ahead after seven minutes but Swansea deservedly drew level eight minutes before the break through Roland Lamah, having created several good chances.
Their dominance increased in the second half but they were unable to turn that into clear-cut openings, with Brad Guzan’s only real save coming from a Jonathan De Guzman free-kick.
Striker Wilfried Bony has not scored since November 10 and never threatened while late sub Alvaro Vazquez has yet to score for the club.
Laudrup said: “We could have done more. It’s good to see some of our attacking players getting confidence.
“Pablo [Hernandez] is coming back and I think he played a very good game. Roland Lamah scored his first goal, which was important.
“Now Bony and Alvaro, they just need to score one or two goals to give them that confidence.
“I think the rest is working. My team is playing the passing game with a lot of confidence, good movement, but the last thing is to create and then to score.”
The form of Bony and Vazquez is doubly important because Michu underwent an ankle operation on Saturday and is out for six weeks.
“Michu scored more than 20 goals last season so we will always miss him but we have to take care of the players who are available and help them, because we need everybody,” said Laudrup.
The result meant Swansea finished the first half of the season in the bottom half of the league on 21 points from 19 games, five clear of the drop zone. Laudrup led Swansea to a ninth-placed finish in his first season and won the Capital One Cup, and he had hoped to do better early in this campaign.
The Dane said: “In my book, we’re a couple of points short. I think after the first six or seven games with very difficult fixtures, I thought we could turn with 23 points.
“But there are many teams down there from 10th to 20th and it’s more or less what I expected. We’ve played 10 away and nine home games so the second half of the season will be the other way around.
“I still think if we get a few more points in the second half of the season, we could end up more or less with the same points as last year, which would for me be a success.”
The draw brought to an end Villa’s run of four straight defeats but there was little comfort for manager Paul Lambert as his players again left the pitch to boos. The Scot hopes key pair Christian Benteke and Ron Vlaar will be fit for the trip to Sunderland on Wednesday but gave little hope that his young side would be boosted by experienced signings in January.
Lambert said: “If we can get one or two back then we can only get stronger.
“Experienced players cost a lot of money on fees and a lot of money on salaries. Never say never but I knew we had to build the club a certain way and that’s what we’ve done. The young lads have given everything they’ve got and that’s all you can ask.”
ASTON VILLA: Guzan, Lowton, Clark, Baker, Luna, Bacuna (El Ahmadi 70), Westwood, Delph, Tonev (Kozak 61), Weimann (Albrighton 79), Agbonlahor.
SWANSEA: Tremmel, Tiendalli (Rangel 55), Chico, Williams, Ben Davies, de Guzman, Canas, Hernandez, Shelvey, Lamah (Pozuelo 68), Bony (Vazquez 84).
Ref: Roger East.