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."
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."
West Ham's head of sports science and sports medicine Andy Rolls insists the trip will not have been used as a holiday.
He said: "We will train over there quite hard - there will be some double sessions and some gym time as well as pitch time. I think we will see the benefits again when we return.
"It has been a long season already and Christmas is always hard and we would been back for six or seven weeks before we played our first Premier League game back in August. The players need a break and a change of scenery."
Some of the West Ham squad remained in England, with defenders James Collins (hamstring), George McCartney (knee) and Joey O'Brien, who went off at Villa Park with a dead leg, continuing their rehabilitation at Chadwell Heath.