The Spaniard wants the Hammers to maintain a level of consistency, after they failed to beat West Brom at home.
The Hammers took an early lead after Mauro Zarate curled a sensational free-kick past Boaz Myhill, but were guilty of making a lacklustre start to the second-half, which allowed the Baggies to equalise as Rickie Lambert's shot deflected off Winston Reid.
And it could have been worse, had the Spaniard not pulled off a stunning save to deny Salomon Rondon from close-range.
Having gone to the Emirates, Anfield and the Etihad and won this season, victories at the Boleyn Ground against the likes of Bournemouth, Norwich and West Brom should have been much more straight-forward games for Slaven Bilic's men.
However, they have only secured three points on two occasions at home in the league this season, and Adrian has encouraged the Hammers to maintain the kind of performance levels that has seen them pull off several upsets already.
"It's difficult to explain because we played really well against the big teams. Against the lower teams we have been putting in the same performances but we just need to concentrate and show the same level against every team," he said.
"We have another good opportunity next week playing at Manchester United - we need to play a great game to get the three points.
"We need to work hard this week to get the three points [on Saturday] and concentrate and give our best level. We have a good team and a good squad," he added.
West Ham's next game - away to Manchester United - will provide them with another opportunity to surprise one of the Premier League elite on their own turf.
And while Bilic will be desperate for his side to stun the Red Devils, he may well be concentrating on the upcoming visits from Stoke and Southampton, as well as the trip to bottom side Aston Villa, as they are the fixtures they need to win if they wish to establish themselves as contenders for a spot in Europe next season.