The Hammers currently sit above the relegation zone on goal difference following their 4-1 defeat against Liverpool at Anfield on Saturday.
The East London club have the chance to get back to winning ways on Saturday when they welcome fellow strugglers Sunderland to Upton Park.
"The last couple of months, we have had some disappointing results but we'll pick ourselves up," McCartney told West Ham's official website. "The spirit around the place is still great and everyone is in it together.
"Like I said, we'll be looking to put in the sort of performance we did against Fulham next weekend against Sunderland and get three points at home again.
"We all know there are no easy games in this league, even though they are below us. It's going to be a difficult game, but it's about how we apply ourselves on the day and we'll be looking to play some positive football and get the win we need."
West Ham have lost four out of their last five matches in the Premier League.