Swansea's Michu cancelled out Patrice Evra's headed opener before Sir Alex's men twice hit the crossbar, had the ball cleared off the line and were denied a penalty appeal in the second half.
"We had a few chances but you have to give Swansea credit as well," club captain Vidic told MUTV. "They fought well and gave everything to get a point out of the game. Overall, I think they played well, we had a few chances and were unlucky."
Vidic, who started his first game for more than three months following a knee injury, said the Reds ultimately paid the price for a sloppy period midway through the first half.
"We started the game well but in that 10 or 15-minute spell after we scored we dropped our performance and Swansea punished us with a goal.
"They had a few good opportunities. After that, we got better and they didn't cause us many
"I think we kept possession well and created a few chances. We just couldn't score a second goal."
– Nemanja Vidic