The one crumb of comfort for Aston Villa was the point that ended a run of four successive defeats and edged the Midlands club further away from the relegation zone. Otherwise this was about as underwhelming as it gets, as Villa toiled for long periods against a Swansea side that controlled the game but badly lacked the cutting edge to pick up a much-needed victory.

How Michael Laudrup, Swansea's manager, must have wished that he could have called upon the services of Michu or Nathan Dyer, both of whom remain sidelined with ankle injuries. Badly missing the goals and creativity that those two provide, Swansea were unable to punish a desperately poor Villa side. It was embarrassingly one-sided for the majority of the afternoon – Swansea enjoyed 73% of possession – yet the reality is that Brad Guzan, the home goalkeeper, had few saves to make.

Villa made the perfect start when Gabriel Agbonlahor put them ahead inside seven minutes but from that point on Swansea dominated the game and it seemed only a matter of time before they equalised. That goal arrived in the 36th minute, when the Belgian winger Roland Lamah opened his account in English football with a far-post header, but Swansea, for all their neat passing, were unable to add a second.

With their next three league matches against Manchester City, Manchester United and Tottenham Hotspur, the Welsh club could come to regret the two points squandered here. As for Villa, their supporters continue to endure rather than enjoy matches at home. They have now witnessed only 11 victories in the last 48 league fixtures at Villa Park and, once again, the final whistle was greeted with some boos.

There is no suggestion that Lambert's position is under threat but the Villa manager made it clear that he does not view the support of the chairman, Randy Lerner, as unconditional. Asked whether he felt immune to the sack, Lambert replied. "Not at all. Never do. I've got a good relationship with [the chairman]. But am I immune to it? No. I always have that fear. I had fear as a footballer and I have that fear as a manager."

Villa are five places but only four points above the bottom three and have what feels like a crunch game away at Sunderland on New Year's Day, although Lambert refuses to accept that his team are in a relegation battle. "Not at all," he said. "The table is so tight at the minute. Halfway there [to 40 points], I don't think anyone can talk like that."

He admitted to feeling relieved that Villa had picked up the point that "stops the sequence of losing, which was vital for us". Agbonlahor's goal - the first Villa have scored at home in the first half this season - arrived after the striker ran on to Andreas Weimann's neat pass before slipping the ball under Gerhard Tremmel. He celebrated by calling all the players over to the dugout for a huddle in what felt like a show of unity.

Swansea, however, were soon exposing familiar Villa weaknesses and the only surprise was that it took Laudrup's side so long to draw level. Ben Davies ought to have scored in the 20th minute but his close-range header bounced over the bar and there was another reprieve for Villa when Jonathan de Guzmán thrashed narrowly wide. Finally Swansea got some reward when Pablo Hernández crossed towards the back post for Lamah to head home via a slight deflection off Antonio Luna.

In the second half De Guzmán forced Guzan to save a 25-yard free-kick and Jonjo Shelvey saw his shot blocked by Luna, but there were few other moments of worry in the Villa defence despite Swansea's superiority. "I think I can say even taking off my Swansea glasses that neutrals would say we should have won the game," Laudrup said.