Carlos Carvalhal’s charges could move up to fourth in the Championship with a home win over the mid-table Bees.
The Owls have been strong in front of their own fans, picking up 34 of their 58 points on home soil this season.
But the atmosphere was a little flat at Hillsborough last time out against lowly Blackburn Rovers, prompting Hutchinson and Carvalhal to issue a rallying cry.
“We are confident wherever we play,” Hutchinson told The Star. “The last game (Blackburn) was difficult because the fans got on our backs straight away. Some people feel that.
“They are great fans but we just need them to get behind us early on.”
After going so close to promotion last year, Hutchinson accepts it was “inevitable” expectation levels would be higher this time around.
He said: “When you do well at any club, fans always expect and we are a big club and have spent a lot of money so I get the pressure.
“They are entitled to voice their opinion.”
Carvalhal says it is the responsibility of the team to give the fans something to shout about but he hopes Wednesdayites will turn out in force this evening.
The Owls head coach, who remains unsure when centre-back Tom Lees (knee) will return to action, said: “I am asking our fantastic fans to push the players as much as they can.
“If you are in a positive environment, the players will respond in one way. If in the work the people give good feedback and push them to do better and better, everybody in the office would do better.
“Football players even more so because they have the crowd and have the environment very near them.
“They have emotions and when the emotional environment is positive, it is normal for players to respond with positives.”
Things are starting to hot up in the promotion race, with just three points separating the four teams in the play-off positions. Huddersfield Town entertain Reading tonight while Leeds United, who host the Owls on Saturday, are not in action.
Hutchinson said: “If we are honest, we always expected to be up there and Leeds and Huddersfield are sort of the surprise packages we were last season so you never know what you are going to get from them.
“They have just carried on winning games which has put the pressure on us to keep going.
“If we can get the three points against Brentford, it is all to play for on Saturday.”