The Toffees looked on course for victory at White Hart Lane when Jagielka's header and a superb solo strike from Kevin Mirallas saw them overturn Emmanuel Adebayor's first-minute goal.
However, Gylfi Sigurdsson scored an 87th-minute equaliser to leave David Moyes' side six points behind fourth-placed Tottenham with seven games to play.
Everton have a game in hand on Spurs and Jagielka believes his side are still in the hunt for a top-four finish.
"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," said the 30-year-old England international.
"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."
On Sunday's game, Jagielka said: "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."