The Northern Irishman took the reins from Kenny Dalglish this summer but Henry has made it clear that there is no repeat of the top-four finish he wanted the Reds to produce under the Scottish icon.
"We don't want to put any pressure on Brendan by saying you have got to make the Champions League this year," said Henry.
"Of course he wants to make the Champions League, we all do and so does every team in the Premier League.
"I thought it was realistic last season but we were so far off that pace.
"At this point we're just trying to get things stabilised - that should be one of our goals."