The second-highest goalscorer in England history made some pointed criticisms of Hodgson's team during Tuesday's 0-0 draw in Ukraine that caused immense irritation.
Although Lineker subsequently backtracked and insisted he was right behind the England chief, he remained of the belief the Three Lions showed a startling inability to retain possession.
However, Lineker indicated on Friday he had spoken to Hodgson.
And, speaking to talkSPORT on Friday evening, the England manager confirmed tensions had now eased.
"I have no problem with Gary at all," said Hodgson.
"I have known him a long time and I understand him as well.
"Reflection changes things and makes us look at other aspects of a performance.
"I am looking at the criticism that we didn't attack as well as we could. I am accepting that as fair criticism.
"Gary is saying we defended well and the discipline is good."
Hodgson conceded that with passions running high in the aftermath of collecting a point that could turn out to be crucial in the battle to reach next summer's World Cup Finals in Brazil, he had reacted in too extreme a manner.
"These things always happen because it is so close to the end of the game," he said.
"It is not a reflective reaction. Once you see the game again you put things in a different perspective."
Chief amongst the wider complaints was that England had shown little inclination to attack after half-time, and seemed happy to settle for a point rather than chase a victory that would have put them within touching distance of automatic qualification.
Instead they must now beat Montenegro and Poland at Wembley next month to make certain of reaching the finals.
"We were so much in control I might have been tempted to throw more attackers on," he said.
"On another day we might have thought let's have a go.
"Jermain Defoe had not played a lot of football either because he had a groin injury.
"Nevertheless we are eight unbeaten and whilst we haven't won the away games it does mean the last two games at home will be very difficult for our opponents."
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