Dundee were promoted to the SPL to fill the 'Club 12' berth created when the application of newco Rangers was rejected. It is the first time The Dee have been in the top flight since 2005.
Lockwood, 35, played in the opening day draw at Kilmarnock and wants the club to go one better in the first home game of the season against St Mirren on Saturday.
"Our home games are going to be vital this season, there's no doubt about that," he told The Courier.
"When you've just come back up after a spell in the First Division, you have to try to take as many points as possible on home turf."
The former Bristol Rovers and Leyton Orient defender moved to Dens Park in 2010 and has called for the home fans to play their part throughout what could prove to be a difficult season.
