Both sides showed attacking endeavour during the opening quarter at the Liberty Stadium, with Swans going close on a couple of occasions before Angel Rangel headed them into an 18th-minute lead.
But Tamika Mkandawire levelled for the Lions just eight minutes later, with the hosts unable to capitalise on chances to regain their lead prior to the break, before an ordinary second half in which Millwall came closest to snatching all three points.
Rodgers said: "We had a good start and scored a terrific goal. It was a great set-piece which worked perfectly. It was a good finish from Angel and I thought it would set us up quite nicely.
"We didn't control the game and in honesty, we didn't deserve much more than a point.
"It wasn't a good game for us."
Source: PA
Source: PA