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
"We shouldn't panic. We are in a good position," Pogatetz said on West Ham TV.
West Ham host Tottenham on February 25 before taking on both Chelsea and Manchester United next month, and the Austrian defender added: "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."
Manager Sam Allardyce used the break in domestic action caused by this weekend's FA Cup ties to take the squad away for some warm-weather training in Dubai.
Last season, it helped rejuvenate the squad for their end-of-season run in, which culminated in a victory over Blackpool in the npower Championship final at Wembley that secured promotion.
Pogatetz, 30, can only see positives from the change in routine.
"When I played in Germany for the last two years, we got a winter break and I think this is a similar break now," he said.
"The lads will enjoy the break and the warm weather. They can recover the bruises and knocks or whatever they have got and then make a fresh start next Monday when we are back. I think the group will really benefit from it."
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- Aston Villa