Hodgson might have been delighted with the performance of his players in Tuesday night's 0-0 draw in Ukraine.
It did not meet with Lineker's approval though.
Roy Hodgson: "I am surprised than anyone who has played for England, captained England and played in games of this nature can be that critical.
"He has done it for the second time.
"I remember Gary Lineker playing. I remember him captaining the team and playing some great games for England.
"But I am pretty sure he also played in some games where it wasn't that easy.
"I don't think every game he played for the England side was a total success.
"I do my best to placate most times but I have just seen a group of players, missing seven first-team squad members beat Moldova 4-0 and come to Ukraine and draw 0-0.
"You can criticise or praise but don't think you are going to put words in my mouth or get me agreeing with these opinions.
"I have been in football for 38 years. I will stick to my opinions, you can have yours and Gary can have his - as can anyone else for that matter.
"This is the beauty of football.
"There are 60 million opinions out there and I will be a little bit surprised when I am walking down the street over the next few weeks if people aren't actually saying you did well in those two games."
Gary Lineker: "Decent result from a team missing a few key players.
"My only criticism, but it's a crucial one, was the inability to pass the ball accurately. Effort, defence, tactics, spirit, all sound.
"Roy Hodgson can't be blamed for some of England's finest having a bad night. With injured players returning his options will be greater.
"He may play Carrick as he's the only natural holding player we have, as well as our best passer. But who to leave out? Age old dilemma.
"Finally, I'd like to make it clear that I'm fully supportive of Roy and think he's doing a good job. Onwards.."