Gabriel Agbonlahor capitalised on some poor Swansea defending to put Paul Lambert's side ahead in the seventh minute at Villa Park, but Roland Lamah headed the visitors level nine minutes before the break.
The men from South Wales dominated possession throughout and manager Laudrup feels his side missed an opportunity to register maximum points.
"Normally when you get a point from an away game in the Premier League - especially if you're a mid or bottom team - you should be pleased," he said. "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, I think we still dominated possession but without creating a lot of chances.
"I said to my players before the game that we had to control it and that we could win.
"Taking off my Swansea glasses, I still think you would say that we should have won this game."
And the Dane admits Swansea have fallen slightly short of the points tally he had hoped to achieve by the season's midway point after amassing 21 from 19 games.
"Twenty one points, in my book, is a couple of points short," he continued. "After the first six or seven games in the league were very, very difficult, I thought we could turn 23 points.
"We've played 10 away games, nine home games. The second half of the season will be the other way around, so I still think if we can get a few more points in the second half of the season, we could end up with more or less the same points as last year, which for me would be a success."
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