West Ham have been beaten by Bournemouth and Leicester City, while Norwich City picked up a draw there in the side's most recent outing.
And Adrian said: "Away we are playing very well but sometimes here at home we need to start much better. We allow the other team to have more confidence and they can score.
"For us, at the moment we are playing better away from home but you have your fans here and of course if you play well, the fans are with you.
"We need a result or to score first to have our fans with us."
The Hammers' squad appears to be designed for playing on the counter-attack, but they are finding it hard to play on the front-foot in the matches.
When they need to take the game to opposition sides, they have shown a few defensive issues and Slaven Bilic will be keen to tighten up the team's backline as the season progresses.
Despite, their slightly disappointing home form, nobody can be upset with the way this season has gone for the Hammers, though.
West Ham are still in third position in the Premier League table, and have picked up away victories against Liverpool, Arsenal and Manchester City already.