The home side created the majority of chances in the first half. Lewis Alessandra looked the most likely to open the scoring, forcing Oxford goalkeeper Ryan Clarke into three saves with shots from distance.
At the other end Oxford threatened with some dangerous crosses from Damian Batt and James Constable and Peter Leven were forced to make vital blocks.
The visitors stepped up the pace in the second period and Barry Roche was the busier keeper making excellent saves from Asa Hall and Batt.
Alessandra once again went close for Morecambe with a shot that flew inches wide of the right hand post with Clarke beaten.
However, the defences remained on top and both sides had to settle for a point.