Pompey have slipped to 19th in the Championship following successive defeats by Leeds and Peterborough.
"The recent couple of losses make this game massive. We can't afford to keep losing - especially at home," midfielder Norris told the club's official website.
"The pressure's on us now and we have to step up to the plate. We have to turn things around.
"There have been a few games this season where we should have got more, but we need to be more consistent.
"As long as we give it our all then the fans accept it, but we really want to play well and win against Barnsley. The game's on TV, so it's a chance to show everyone watching at home just what we can do."