An own goal from Xabi Alonso and Spanish from a Tuncay Sanli in the second part dealt the fatal blow to the team of Rafael Benitez.
Liverpool still seven points of leader Manchester United, which has 62 points and one match remaining. In addition, the team "red" fell to third place behind Chelsea's win over the Wigan Athletic 2-1.
"Before the match was difficult and now is even more difficult. We'll see what happens against Sunderland and try to improve, but now depends on United," admitted Benitez.
"If you want to stay on top of the table you have to dial. I do not mean much because for me it is clear that in the first twenty minutes we had five situations and we must seize if we win."
"We had some problems and injuries, some players were tired, but we had chances and control the first thirty minutes. Middlesbrough were better in the second half," the technical "network's", not with Fernando Torres after the Spanish suffered an ankle injury in the victory for the Champions League mid-week before the Real Madrid.
Chelsea opened the scoring through John Terry for 25 minutes, but eight minutes after Kieron Dyer was able to equalize the scoring for Wigan. Frank Lampard ended a victory "blue" time complementary.
Meanwhile, Arsenal today suffered its fourth consecutive tie the match with goals at home to Fulham. The result left Arsenal in fifth place, two of Everton, who sank a little more today at West Bromwich Albion in the last position of the table from the English Football League defeat 2-0.
Australia's Tim Cahill and Frenchman Louis Saha set the team goals for Liverpool, which is sixth with 44 points.
Cahill pitch to launch a corner goal nine minutes before the break, while Saha, who was returning to the team after an injury, closed the scoring at 70 minutes.