The Reds took a narrow 1-0 lead into the away leg in Trabzon which was soon cancelled out by Teofilo Gutierrez' 4th minute goal but they rallied to score twice in the final six minutes, through an own goal and a Dirk Kuyt winner to book their spot in the initial phase of the competition.
Hodgson said relief was the main emotion he felt after watching his side battle to a character-building win without players like Steven Gerrard, Fernando Torres, Maxi Rodriguez, Daniel Agger and Milan Jovanovic.
"We were looking down the barrel here coming to Trabzon," said Hodgson.
"They were fresh off a win over Fenerbahce here, they are last season's champions, they don't lose at home and we beat them at home.
"To get a result here was something quite important and will stand us in good stead for plenty of other matches.
"We had the toughest possible start but I thought we got over it and throughout the game played well.
"Quite frankly we should have had the game sewn up long before we did.
"But I was relieved."