All four goals arrived in a 25 minute period in the first-half as Paco Alcacer cancelled out Pablo Sarabia's opener yesterday.
Angel Lafita then put Getafe back in front only for substitute Santi Mina to level once more.
A draw leaves Valencia still six points off the top four, but does at least preserve their unbeaten home record in the league stretching back to November last year.
"We made things too complicated," said Neville.
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"We have to repeat performances like these in every game. When you give everything in a match you want to achieve the best result and today we wanted to win.
"We are working hard and I know that the results will follow."
Neville had managed to get his first win in three attempts against third-tier Barakaldo in the Copa del Rey in midweek.
But, just as against Eibar in his first taste of La Liga action last weekend, Valencia made a poor start and were behind after just 10 minutes.
However, the hosts reacted quickly to going behind as Alcacer caught Joao Cancelo's cross from the right sweetly to register his seventh goal of the season.
Yet, Valencia were still incredibly open at the back and were behind again midway through the half when Aymen Abdennour needlessly gave the ball away and Lafita smashed home a loose ball from just outside the box.
And it seemed Neville had suffered another setback when
Yet, that proved to be a blessing in disguise as Mina replaced the full-back and equalised with his first touch as he swept home Alcacer's cross at the back post.
The hosts then looked the more threatening side for large spells, but were denied by former Valencia 'keeper Vicente Guaita as he produced great saves to deny Danilo and Dani Parejo either side of the break.
Neville introduced former Manchester City striker Alvaro Negredo in the search for a winner and he had a golden chance when he headed straight at Guaita three minutes from time.
Elsewhere, Betis and Sevilla played out a bore 0-0 draw in a bad-tempered first Seville derby for 20 months which saw 12 bookings and few clear-cut chances.
Lucas Perez scored for the seventh consecutive league game as Deportivo la Coruna maintained their push for European football with a comfortable 2-0 over Eibar to move to within two points of the top four.