Jagielka rescued a point for Everton with a ferocious strike from long range in stoppage time at Anfield, after Steven Gerrard's 65th-minute free-kick had looked set to prove decisive.
Having described his side's leveller as the best goal he has seen live, Martinez hailed Jagielka's efforts in bouncing back from a tricky start to the season.
The 32-year-old lost his place in England's team for this month's matches with Norway and Switzerland and has been part of an Everton backline that has shipped goals all too easily in the opening weeks of the Premier League campaign.
"When you see someone like Phil Jagielka taking responsibility, someone who has got a lot of unfair criticism from the outside, that's a real example of how to face adversity, take responsibility and no-one deserves more than him the feeling of scoring such a special goal in front of the Kop," said Martinez.
"That's as good as I've seen. I don't think I've seen a better strike in live football.
"When you see him connecting with the ball, I think the body is leaning back a little bit, and you're thinking it has to be an incredible strike to put it in the top corner. And it was
"It helps that it's in the last minute, it's at Anfield and it's for my team - that's why maybe it's the best strike I've ever seen."
Invited to elaborate on his thoughts regarding the recent criticism of Jagielka, who started England's first two games at the World Cup in Brazil, Martinez added: "When you are looking at some of the reports about his England performances - and obviously he was the one who didn't play in the next two games when the national team got together - and because of our defensive record this season, there's been a lot of talk about a World Cup hangover.
"I felt that has been really unfair. He's been someone that has set really high standards in our football club.
"He cares like nobody [else], but today I was so, so proud because it would have been easy for a centre-half to just stay in his position and not do anything about it [the scoreline].
"I think the way he conducted himself on the pitch, looking for that equaliser, is just an example of his belief in himself, the responsibility he has and the way to face adversity."
Martinez faces an anxious wait to discover the extent of a hamstring injury that forced Kevin Mirallas to be withdrawn in the first half of Saturday's game.
"It seems a bad hamstring, a bad soft tissue [injury]," he added.
"We're going to assess him in the next 48 hours but that was a real problem for us.
"It's unfortunate that we [have] lost someone like him, someone like Ross Barkley, someone like Steven Pienaar, someone like Seamus Coleman - very important players that we need to get back as quick as we can."
