The Uruguayan, who'd already scored in the first half had the perfect chance to score his second and Liverpool's fourth against Toulouse as he found himself clean through on goal.
He did all the hard work by getting past Toulouse defender Rasmus Nicolaisen, rounding goalkeeper Guillaume Restes, however, with an open goal gaping, Nunez's effort came back off the post.
Fortunately for him, Reds midfielder Ryan Gravenberch came in on the rebound and slotted home with his left foot.
Moments later Nunez was substituted and had a little giggle with Liverpool manager Jurgen Klopp, no doubt reflecting on that sitter of a chance.
Klopp's men were good value for their 5-1 triumph in the Europa League, Diogo Jota, Wataru Endo and Nunez netting in the first half to put Liverpool 3-1 up, while Mohamed Salah scored in stoppage time.
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Klopp had promised to make 'not too many' changes to his side following Saturday's 2-0 win over Everton in the Merseyside derby, but there were only three survivors in the starting line-up - Jota, Gravenberch and Trent Alexander-Arnold.
Klopp had also said he wanted to ensure Toulouse, who lost 4-0 on their only previous visit to Anfield in 2007, did not enjoy their evening and all three of those players had a big say in making sure they did not.
Jota got the opening goal, Alexander-Arnold the assist for the second and Gravenberch, a driving force throughout in Liverpool's midfield, creating the third before scoring the fourth, but this was also a show of the depth in Klopp's squad.
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Jota opened the scoring with only nine minutes gone. Joe Gomez prodded the ball forward to the Portugal international, who turned on the edge of the centre circle and ran at goal, holding off two opponents and skipping past Logan Costa before beating Guillaume Restes with a low shot.
Liverpool, dominant on the ball and winning the midfield battle, looked poised for a comfortable night, but Toulouse then gave their noisy travelling support a moment to savour, hitting their hosts on the break with quarter of an hour gone.
Aron Donnum turned on the halfway line to play in Dallinga, being kept onside by Alexander-Arnold and he had space to run at goal before slotting a shot under Caoimhin Kelleher.
Liverpool soon regained their composure. Gravenberch almost scored a remarkable goal in the 28th minute, controlling a raking pass from Alexander-Arnold, breaking into the box and then - having seemingly run into traffic - twisting his way through to test the 18-year-old Restes with a low shot.
Moments later, Endo's moment arrived as the Japan international got in front of his man to direct Alexander-Arnold's cross into the corner of the net.
Toulouse were rocked and soon fell further behind. Gravenberch drove at goal from his own half, laying the ball off for Curtis Jones to shoot from a central position. His effort was charged down but the ricochet fell for Nunez, whose emphatic finish found the roof of the net.
There was a scare at the start of the first half as Kelleher got a clearance all wrong, leaving Gabriel Suazo with what should have been an easy chance, but he shot straight at Alexander-Arnold on the line.
Liverpool's fourth came about in almost comical circumstances in the 65th minute. Jota's pass found the run of Nunez, who had done the hard work by rounding Restes, only to see his shot come back off the post.
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Nunez still had his head in his hands as Gravenberch picked up the pieces to get the goal his performance deserved.
Cody Gakpo then replaced Nunez in a flurry of substitutions, making a welcome return from a knee injury, while there was also a late cameo for Salah, who scored his ninth goal in 12 appearances for Liverpool with almost the last kick of the game.
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