Despite winning the Carling Cup and making the FA Cup semi-finals, five defeats in the last six Premier League matches have rendered the club's aim of qualifying for the Champions League a distant dream.
A home defeat by relegation-haunted Wigan on Saturday was the latest disappointment, and Liverpool now trail fourth-placed Tottenham by 13 points with just eight games remaining. They are also eight points behind Newcastle, who are sixth.
The Reds were booed off after their defeat by the Latics while Dalglish found his judgement, signings, tactics and suitability for the job all questioned. The Scot blamed their tenth defeat of the Premier League season on tiredness but Enrique believes the squad must address the situation.
"The manager takes pressure for us and of course that is good,'' the Spaniard said. "But the truth is, when we make mistakes or have a bad game, we know where the mistakes come from.
"Who plays the games? The players. Who has to win them? The players too. The players are frustrated just the same (as the fans). We have played good football in many games but against Wigan we didn't deserve to win.''
Spaniard Enrique was one of seven summer arrivals and is in the minority having largely escaped criticism of his performances, with Jordan Henderson, Andy Carroll and Stewart Downing bearing the brunt of the flak, largely due to their hefty price tags.
It has left many questioning Dalglish's transfer choices but left-back Enrique is naturally keen to repay Dalglish for bringing him to Anfield from Newcastle. "I am really grateful to him,'' said the 26-year-old.
"Of course I want to do my best for the team and for Liverpool first, but also for the manager because he signed me.''
Enrique thinks the side need more time to gel but accepts that seventh is not good enough for a club of Liverpool's standing. Even if Dalglish's side can add to their Carling Cup triumph, which ended a six-year trophy drought, with another piece of silverware, criticism will still remain over their league form.
"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 told the club's official website.
"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.''