It was a meeting of two out-of-form teams, with Villa having lost their previous four matches while Swansea were without a win in five.
The hosts scored in the first half at Villa Park for the first time this Barclays Premier League season through Gabriel Agbonlahor in the seventh minute but Swansea piled on the pressure and got their reward when Roland Lamah equalised eight minutes before half-time.
The Welsh side dominated the second half but were unable to find a winner.
Laudrup said: "Normally when you get a point from away games in the Premier League, especially if you are a mid-table or bottom team, you should be pleased but I think after our first half we should have won the game.
"Even conceding an early goal, we came back, dominated completely, created chances, scored the equaliser and could have scored one or two more.
"Second half we still dominated in possession but without creating a lot of chances. Villa did not have any chances at all.
"Even taking off my Swansea glasses, I still think as a neutral you would say that we should have won this game. I think they're quite happy with a point."