Since being promoted to the top flight the Canaries have failed to prevent their opposition from finding the net in the opening eight matches of the season.
Next up for Paul Lambert's side is a match against Swansea City on Saturday and Martin is hopeful that Norwich can secure their first shut-out of the season from the Carrow Road fixture.
"We deserve a clean sheet the way we've played the last few games," Martin told the club's official website.
"Hopefully, we'll get one sooner rather than later and we'll keep building."
Martin joined Norwich on a permanent basis from Peterborough United in 2010.