Steven Gerrard described his hat-trick in Liverpool's 3-0 win over Everton – the first for 30 years in a Merseyside league derby – as "extra special" but warned his team-mates that they must now produce similar results on a consistent basis.

Liverpool had lost their previous three league games to slip out of realistic contention for a top-four finish and Gerrard said after his side's convincing performance at Anfield: "It's been frustrating, the inconsistency we've been showing in the league, very frustrating. We played very well [against] Arsenal and got nothing, then we never turned up at Sunderland [on Saturday, going down 1-0].

"We're going from one extreme to another at the moment. We need to find a level of consistency where we go on a winning streak, rather than win one and lose one, because otherwise we find ourselves in a position in the league that we don't want."

Gerrard's hat-trick, the first by a Liverpool player against Everton since Ian Rush scored four in a 5-0 win at Goodison Park in November 1982, came on his 400th league appearance for the club. "To beat Everton is always special, so to get three goals is a little bit extra, but I have to give my team-mates a special mention, especially Luis Suárez who put two goals on a plate for me," he said. "It was a great team performance, a clean sheet. Everything we wanted from the game we got it."

Gerrard believes he can build a formidable relationship with Suárez: "I haven't played with him much but when we do we seem to have an understanding. With Andy [Carroll] as well. I think the three of us in the starting XI are always going to be a threat. Hopefully that can continue to get stronger and stronger."

Kenny Dalglish echoed Gerrard's call for positive results to be maintained until the close of the campaign, which continues with an FA Cup tie against Stoke City on Sunday. "The season's not finished because we won the game," the manager said. "We've got to carry on and do the best we can to win more games and if we do that – compete like that – I'm sure we will but then they have done in many games here this season.

"It was a fantastic performance. I think the result reflected the performance and for us we're delighted that at last we've got the reward for a great performance, one of the many we've had here but we got the real reward for the effort they've put in tonight.

"It's always nice when you play really well and win. Sometime it's even better when you're rubbish and you still get three points. But that's not happened to us too often this year."

Dalglish admitted it was positive for the club to return to victory in the league, with the last time Liverpool were defeated four times in a row being under Gérard Houllier a decade ago. "It's nice to get back to winning ways. I think we always believed in the way we play, and we still will believe it," he said.

Of Gerrard's three-goal contribution Dalglish said: "For a guy who left school at 15, my vocabulary is not that great. There is no way I could extol the virtues of Steven Gerrard and do him justice.

"He's been fantastic for this football club – three goals was a fantastic reward. It was a team [effort] but somebody got three goals so rightly Steven will get a lot of the headlines. But he'll be the first one to say he wouldn't have been there with three goals without the help of the others.

"I think the most important thing for us, and I think Steven would say the same thing, is that we've got three points and they've put a fantastic performance in. They've had to compete really hard against an Everton team who have been going really well.

"It's a good reward for the players and its great they maintained the belief in themselves and the philosophies we've got and the way we've been playing and I don't think it will do them any harm. But we've got a difficult game coming up on Sunday so we can enjoy this for a couple of days and the look forward to Sunday, but they should be pleased because they were fantastic.

"I'm not going to sit and go through every single player; every single contribution was magnificent. They all did fantastically well and if you don't compete against Everton you're not going to win three-nil."

David Moyes, who reaches 10 years as Everton manager on Wednesday having still not won at Anfield, said of the defeat: "We gave away three terrible goals – that led to our downfall tonight."

Moyes made six changes from the team who beat 1-0 Tottenham Hotspur in the league last weekend, possibly with Saturday's FA Cup quarter-final against Sunderland in mind. "We have got a big week," he said.