Hart was criticised for both goals conceded by England in their 2-2 draw with Switzerland.
Wilson said, "I was almost offended by good journalists saying here we go again England.
"You look at the goalkeepers who have been ridiculed in the last two or three years and they are just jumping on the bandwagon.
"For the first goal, once the ball is played into that area with defenders trying to defend it and attackers trying to get their heads on it, if Joe reads it and follows the line of the ball and someone heads it in the other corner he would just look a mug.
"So when no head makes contact, and it was a great delivery, he just didn't have the time to react - I certainly wouldn't point the finger.
"For the second goal, I actually thought Joe did well to make up the ground and nearly keep it out. He was covering the back five yards of the goal and wall was supposed to be covering the three yards on the near side.
"James Milner, for some obscure reason, moved from his position in the wall and Joe has got to make up five yards and improvise and he almost kept it out - he nearly bailed Milner out.
"Joe is going to be England's goalkeeper for many years to come. He is an incredibly strong character and he is going to take this on the chin."