The Bulldogs defended tirelessly and led 4-0 at the break, only going down to two quick-fire tries from Shaun Lunt after an hour.
Huddersfield were given a big fright and Kear said: "I thought our players were magnificent. We can certainly defend and the most we have conceded this season is 18 points."
He added: "This is what the Challenge Cup is all about. I can't fault Huddersfield because they were very respectful to us and played very well. Anybody who paid their £15 have had their money's worth."
Batley pinned Huddersfield down in the first half playing with the infamous Mount Pleasant slope. The Giants struggled against Batley's spirited tackling and rarely got out of their own half.
The hosts deservedly took the lead two minutes before the break when Gareth Moore set up Gareth Potts. Moore missed the conversion but Batley went in at half-time 4-0 up. The Giants, with the supposed benefit of the slope in the second half, continued to be thwarted by the tough Kingstone Press Championship part-timers.
The Bulldogs, who gave the Giants a fright at the same stage of the competition two years ago narrowly going down 28-18, were finally undone by two tries in two minutes by Lunt. Danny Brough converted one of the two scores and then kicked a late drop goal and a penalty to spare the Giants an embarrassing defeat.
Kear said: "I am really chuffed with the players. It's up there with the best we have played this season and hopefully we can take this form into the league. The players worked hard to the end and what you can't afford to do is die wondering. We threw everything at them and we performed like champions."
Giants coach Paul Anderson was just relieved to go into the hat for the fifth round and said: "It's the Challenge Cup and that's what it's all about. We did not expect Batley to lie down and roll over. It was a good, old-fashioned Challenge Cup game. What Batley did was challenge us in many areas but we found a way to win.
"There were parts of the game I was disappointed with and we didn't get a flow going but I don't want to take anything away from Batley. They were excellent. It's all about Batley. They had no pressure and they have had a decent crowd and pushed a top two Super League club all the way."