The Hammers' 2-1 defeat at struggling Aston Villa was a fourth loss in six league games and left them in 11th place, with a seven-point cushion above the relegation zone heading into the final 12 matches of the season.
West Ham host Tottenham on February 25 before taking on both Chelsea and Manchester United next month.
Austrian defender Pogatetz, who has signed on loan from Wolfsburg, is confident Sam Allardyce's men have what it takes to steer themselves away from trouble.
"We shouldn't panic. We are in a good position," Pogatetz said on West Ham TV.
"Obviously we know we have hard games coming up, but we are up to the task.
"Our performance was all right at Villa 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."