The England central defender helped David Moyes' side gain a first victory of the campaign at St Andrew's courtesy of an own goal from Roger Johnson and a Tim Cahill header.
It moved the Toffees off the bottom of the Premier League after they had collected only three points from the opening six matches.
Now Jagielka, who is set to be named in Fabio Capello's squad tomorrow for the Euro 2012 qualifier with Montenegro, is looking for Everton to climb the table.
The former Sheffield United player said: "The slow start we've had this season has been very baffling.
"Most people have seen us start quite slow before but I don't think we've started quite as slowly as this.
"It was an uncomfortable position to be in and all the boys knew we had to turn the corner somewhere.
"Thankfully luck was on our side for the first (own) goal. Hopefully it will be a turning point."
Jagielka knows one victory does not make up for the poor start to the season and that there is still much work to be done.
He said: "We hope it will be onwards and upwards from this point. That is the plan. The gaffer will have us in, working hard.
"We are happy to have got these three points but we know there is still a long way to go to get to where we hope to be in the league.
"It is going to be a tough next couple of months."
Moyes admits it is second nature to a manager in having to deal with the pressure of being at the bottom - and top - of the table.
He said: "If you are at the top, there is a pressure to stay there, if you are at the bottom there is a pressure.
"When you are in the world you work in, it's something that is part and parcel of the job.
"The bit we are surprised with is that the results haven't been better.
"When you are bottom of the league, I wouldn't say you panic, but no manager likes being there.
"I am no different - and especially with the team I've got and the expectations I have got of the team."
Jagielka must wait to see if he will hold onto his England spot now that John Terry and Rio Ferdinand have returned to fitness.
But he was happy with his performances in the previous Euro 2012 qualifiers with Bulgaria and Switzerland and has started the past three internationals.
He said: "All I could do was try and give the manager something to think about. The manager chooses what players he wants to play.
"We won two (qualifying) games, did pretty well as a team and I was been part of that team.
"There was not much else I could do. I was happy with the way I've played.
"I'm still learning about international football so hopefully I will get some more opportunities to keep learning."
Birmingham tasted defeat at home for the first time in 13 months and manager Alex McLeish was unhappy with the boos which greeted his team at the final whistle.
He said: "I don't think any of us deserved the reception (at the end).
"I don't think it was fair the fans should boo us for losing the game or indeed the performance because it wasn't a bad performance.
"The players deserve a lot of credit for what they've done over the past year.
"It is the culture we live in. Players are paid big wages and the fans are expecting them to deliver.
"You can't blame them for that. We do live in a society where every little move is scrutinised.
"There is no doubt there is more fickleness than ever before.
"We have to take it on the chin. I don't think we should have been booed and that's all I'm saying on it."
Source: Team Talk
Source: Team Talk