The 1-0 defeat at Sparta Prague left Puel’s side needing a win or scoreless draw against Hapoel Be’er Sheva in their final group game to progress in the competition.
But it was the nature of the performance in the Czech Republic that caused the Frenchman most concern.
And the Southampton boss knows Saints must improve significantly if they are to deny former manager Ronald Koeman victory when the Dutchman returns to St Mary’s Stadium.
“It was a disappointment of course with the result and also with the quality of our game,” said Puel. “It was not sufficient to win this game, and a draw was not sufficient for us –- only a victory, but that was not possible.
“It’s important to keep a positive attitude, because we stay with our destiny in our hands, and this is the most important thing.
“Now it’s important to come back in the Premier League with good spirit, good attitude and a good recovery, of course.
“I think we have got to play a good game, because it is an important one –- it is Ronald Koeman’s team and it’s a good challenge for us.”
Jose Fonte and Dusan Tadic were both sidelined in midweek, but Puel is hopeful centre-back Fonte will recover from a foot injury in time to face Everton.
“Tadic we are going to see if he can train,” said the manager. “Normally I think that it is not possible, because his injury was a bad injury and it’s a problem for us.
“Jose I believe can play, but Dusan no. Now he’s two weeks without a training session and at the moment it is difficult for him.”
Koeman hopes Southampton fans show him “respect”upon his return to the south coast.
The Dutch great quit the Saints to replace Roberto Martinez in the Goodison Park hotseat and is expected to receive a hostile reception from the home supporters at St Mary’s.
– ‘Big club’ –
“I cannot change the opinions and feelings of the Southampton fans — I hope they will respect me,” said Koeman.
“After my career, I will look back and say I had a great time there. Of course, I understand the difference of opinions and reactions. I’m not afraid of that.