The Owls, who won automatic promotion last summer after spending two seasons in League One, are one point clear of the bottom three following three defeats in their last four matches.
Dave Jones' side face relegation rivals Barnsley and Bristol City in the space of three days after the international break, with the South Yorkshire derby at Hillsborough on March 30 followed by a trip to Ashton Gate on Easter Monday.
"The next two games are massive," Pugh told the club's official website. "There is no hiding away from how big and important those fixtures are for this club.
"We know we can't rely on any other team, we've got to concentrate on our own form, our own results and do everything we can to battle our way out of this position."
Pugh, who joined the Owls on loan from Leeds in January until the end of the season, added: "After losing a game you always want to get on with the next one as soon as possible.
"We've got some massive games ahead and are playing a lot of the teams that are around us.
"There's plenty to play for, plenty of points on the line and we're confident we can collect enough of them to climb up the table."