The club's shock 2-1 defeat at home to Wigan on Saturday was their fifth loss in their last six league matches, leaving any remaining hopes of finishing in the top four remote.
Manager Kenny Daglish has borne the brunt of the criticism in the wake of recent results, but Enrique insists that the culpability lies with the players.
"The manager takes pressure for us and of course that is good," the 26-year-old told the club's official website.
"But the truth is, when we make mistakes or have a bad game, we know where the mistakes come from.
|THE REDS' ROUGH RUN
Liverpool's league form
||Man Utd 2-1 Liverpool
||Liverpool 1-2 Arsenal
||Sunderland 1-0 Liverpool
||Liverpool 3-0 Everton
||QPR 3-2 Liverpool
||Liverpool 1-2 Wigan|
"We have played good football in many games but against Wigan we didn't deserve to win."
A Liverpool win with over 2.5 goals scored in the match when they face Newcastle on Sunday can be backed at 11/4 with Bet365.
Enrique was one of seven summer signings made by Dalgish, many of whom have come in for criticism.
The likes of Jordan Henderson and Stewart Downing, signed for a combined £36 million, have been singled out by some as expensive flops alongside misfiring striker Andy Carroll, who joined the club last January for a £35m fee.
Enrique, though, is adamant that he wants to improve his club form in order to repay his manager for bringing him to the club last year.
"I am really grateful to him," he added. "Of course I want to do my best for the team and for Liverpool first, but also for the manager because he signed me."
The Reds have enjoyed some success this campaign, lifting their first trophy in six years in February after their League Cup triumph over Cardiff City.
|"The players are just as frustrated [as the fans] ... Against Wigan we didn't deserve to win"
- Jose Enrique
With an FA Cup semi-final spot already secured, the former Newcastle left-back is pleased with his side’s progress so far this season, particularly considering the number of new faces at the club.
"In the cups we are doing well. Liverpool went many years without winning something and already we have one cup and we are playing for another one," he observed.
"In the league I think we deserve more than where we are now but the truth is we are in seventh position.
"This team is in production; the owners have signed young players. I think we have a really good squad already but of course we have to improve - everyone."