The Hammers suffered a fourth defeat in six games last weekend when they lost 2-1 at Aston Villa, leaving them seven points above the Premier League drop zone.
Games against Tottenham, Chelsea and Manchester United are on the horizon but defender Pogatetz is confident they can stay clear of trouble.
"We shouldn't panic. We are in a good position," said the Austria international.
"Obviously we know we have hard games coming up, but we are up to the task.
"Our performance was alright 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."
West Ham boss Sam Allardyce used the break in domestic action to take his side away for training in Dubai.
Last year it helped rejuvenate the squad for their end-of-season run in, which culminated in promotion to the Premier League via the play-offs, and Pogatetz can see the 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."