The German has urged his team-mates to push on after just two defeats in 22 games, and victory on Monday against Southampton may well propel them into a Champions' League spot
The Toffees travel to the south coast to take on opponents who are in a transitional phase after sacking manager Nigel Adkins on Friday. Argentine Mauricio Pochettino has taken over the reins for the Saints, and Hitzlsperger hopes Everton can capitalise on that and secure victory, but is expecting a tough game.
"People will be watching us and expecting a lot from us because we've played so well in the past, and that's what we've got to justify," he told the club's official website.
"There is a lot of confidence among the players now with the results we've had, but we definitely won't underestimate Southampton. They're fighting for every point, they want to stay in this league and they're a good footballing side.
"But we have enough confidence to go there and say we want to win this game, and we've got every chance to do so."
It will be Everton's first visit to St. Mary's since 2005, and victory could well put them into fourth place if Tottenham fail to get a positive result against Manchester United on Sunday. The Toffees beat Southampton 3-1 in the reverse fixture earlier this season, and Hitzlsperger is hoping for a similar outcome on Monday.
"When I watched them play here at Goodison Park, they started really well and they gave us a tough time for the first 20 to 25 minutes," he said.
"It took us a while to break them down but I think once we'd done that we made it look easy in the end. But they've got some very good footballers in their side so we've got to be prepared and switched on."
The German is keen to add a few goals to his game, having failed to get off the mark so far for his new club.
"I'm very keen to score because obviously that's a bit extra," he added. "Scoring a goal for your team is always quite special, especially when you're not a striker.
"I've always enjoyed trying to hit the target and scoring goals, so hopefully it comes around quite quickly."