Everton looked on course for a shock but deserved victory when they went 2-1 ahead thanks to Jagielka's header, and a superb solo goal from Kevin Mirallas, but Gylfi Sigurdsson's 87th-minute equaliser stole a point for Spurs. The result means Everton are now six points off fourth-place Tottenham, although the Toffees have a match in hand against Arsenal on April 16.
Everton also have to face Liverpool and Chelsea before the end of the season, but Jagielka insists Champions League qualification is still not out of reach. When asked if Everton are still in the hunt for the top four, the England centre-back said: "Yeah, I think so."
He added: "We know we need a lot of help from teams around us, either taking points off each other or a shock result coming in. But we'll take that.
"We've not been in as good a position in the league for a long time - we're usually chasing fifth or sixth - so it's nice to have gone up a level and as much as we're delighted with the point we'd have loved to have three.
"But we'll go on to next week's game and keep the chase on for as long as possible."
Tottenham struggled to contain the pace and power of Victor Anichebe while at the other end of the pitch Jagielka and Sylvain Distin kept Emmanuel Adebayor quiet for most of the game.
The lateness of Sigurdsson's equaliser meant manager David Moyes left north London with a tinge of disappointment, but Jagielka insists the team should be proud of the draw.
He added: "It was a well-earned point in the end. Spurs have got a fantastic team, fantastic players and a fantastic manager.
"It was always going to be tough for us to come here. We would obviously have loved to have lasted a few more minutes and taken the three points but realistically, especially the way we started the game giving them a goal start, a point in the end is obviously a good result."
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