The Toffees' campaign has been one of frustration and inconsistency, with an expected challenge for a European place not materialising. Fears of relegation have all but been extinguished by Saturday's hard-fought 2-1 win over Fulham at Goodison Park, which lifted David Moyes' men to 40 points in the Barclays Premier League.
Jagielka said: "I was really excited about the start of this season but unfortunately we didn't start the way we wanted to. It snowballed and we didn't pick up many points. As much as I don't want to rule out the rest of this season, I can't wait for the next."
He added: "We have got some exciting players and hopefully the gaffer can add to that and we have a decent pre-season and, for once, a decent start to the season."
Jagielka, 28, certainly plans to be a part of any future Everton success having committed himself to a new four-year contract on Friday.
The England international added: "I'm delighted. There was talk about it from the summer onwards and it was easy enough to sort out.
"I was happy to stay and the club wanted me. It wasn't too much hassle."
Saturday's encounter began at end-of-season pace, despite both sides having another eight games remaining. That changed when Seamus Coleman punished Fulham for their lack of urgency by heading home the opening goal 10 minutes before the break.
Former Fulham striker Louis Saha doubled the advantage early in the second half but the visitors finally stirred to prevent Everton cruising to victory. Clint Dempsey pulled one back on the hour and Everton had to withstand considerable late pressure to claim the three points.
Jagielka, who might have made victory more comfortable had Carlos Salcido not cleared his late header off the line, said: "Obviously we are not 100% safe yet but I think there are probably too many teams down there for us to be considered relegation material. I think we are looking upwards now rather than behind us but there are not many more places where we can climb."
Source: PA
Source: PA