The Hammers currently sit 11th in the top flight, seven points clear of the relegation zone, but have lost five of their last seven league games.
And, after the Austrian made his debut on loan from Wolfsburg in a 2-1 defeat to Aston Villa, he has insisted his new teammates have enough quality to stay up.
"We shouldn't panic," Pogatetz told West Ham TV. "We're in a good position. Obviously we know we have hard games coming up, but we are up to the task. On Sunday our performance was all right and if we can push on from that, we can put many more points on the board and achieve everything we want by the end of the season."
Pogatetz made his first start in English football for three years at Villa Park on Sunday, and expressed delight at marking his return.
"Of course, for me personally it was great to be playing again in the Premier League," he said. "To be playing for a big club such as West Ham, who you see so many supporters follow away from home, was great for me.
"Unfortunately the result didn't go our way so I'm disappointed, but I hope to be involved more so I can play many more games for West Ham and help us to achieve our targets this season and get some more points on the board."
The former Middlesbrough center back also claimed that Sam Allardyce's men deserved more from their clash with the Villans.
"I think we probably deserved at least a draw," he added. "We created a lot of chances but the ball just didn't want to go in. Then they scored from a penalty first and, after that, it was difficult.
"Even in the end stage of the game, we had two incredible opportunities to equalize so it was disappointing that I lost on my debut. For the team, I think we deserved more. Our performance, especially in the second half, was good so I'm a little bit disappointed about that.
"We played 3-5-2 for a few minutes and then we had to change it around anyway because we lost Joey [O’Brien] to an injury. We had to switch it around a little bit but we couldn't play that way for too long, so in the end we switched back to four at the back and I think we adapted quite well because we didn't give too many chances away. It was unlucky that we didn't score first because, if we had, I think we would have gone on and won the game."
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