Match of the Day presenter and former England skipper Lineker was frustrated by the goalless draw in Kiev.
But Hodgson has defended his tactics and questioned Lineker's observations.
"I am surprised that anyone who has played for England, captained England and played in games of this nature can be that critical," Hodgson said.
The point in Ukraine keeps England top of World Cup qualifying Group H.
Victories in their two remaining matches at Wembley, against Montenegro on 11 October and Poland four days later, will secure automatic qualification for next year's finals in Brazil.
Hodgson said he told his players to bypass midfield in the early stages of the game in Kiev.
England's second highest goalscorer behind Sir Bobby Charlton, Lineker - who netted 48 times in 80 caps between 1984 and 1992 - said in a Tweet on Tuesday that he later deleted that Hodgson's side were "awful" and added: "What happens to some of these players when they pull on an England shirt?"
The Ex-Tottenham, Everton and Barcelona striker, who said England's tactics were "a step back to the dark ages" against the Republic of Ireland in May, subsequently insisted he was fully behind Hodgson as he moved to clarify his comments.
He said: "I'd like to make it clear I'm fully supportive of Roy and think he's doing a good job."
But Hodgson added: "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."
Asked about his tactics in Ukraine, Hodgson said: "Did we play longer balls forward early? Yes, we did.
"We didn't want to play out from the back and invite pressure."