In a game which saw both sets of defenders on top, Morecambe created the better chances but failed to find the target as they looked for rare back-to-back home wins.
The best openings fell to Lewis Alessandra in the second half, with one effort from the right side of the penalty area fizzing just over before he missed the best chance of the game when he was one-on-one with Stuart Tomlinson but lobbed over the bar.
Burton only tested Morecambe's debutant keeper Andreas Arestidou once throughout the 90 minutes, with a long-range shot from Jacques Maghoma forcing the former Preston keeper into an uncomfortable save.
Maghoma drilled a first-half shot into the side-netting but Albion's only effort of note in the second half was a long-range Robbie Weir shot which flew well wide of a post.
Morecambe finished the game on the front foot but Jack Redshaw and Andy Fleming both fired horribly wide from good position.