Southampton's James Ward-Prowse looks dejected after Sparta Prague's Costa Nhamoinesu scores their first goal
The Saints lost 1-0 away to Sparta Prague on Thursday to set up a crucial showdown at home to Hapoel Be’er Sheva in their final group game.
With the two sides level on seven points, Southampton must beat Hapoel or draw 0-0 to seal qualification to the knockout stages, with their goal difference superior and the two teams drawing 0-0 back in September.
Puel is confident his side can do just that and they owe it to their supporters to qualify in style following their defeat to Sparta Prague.
“We hope to give our supporters a good feeling and the pleasure of qualification, because that is what we all want,” Puel told the club's website.
“We have to prepare for the final game now at St Mary’s. It’s clear it is a very difficult group, with Inter finishing bottom of the group.
“We will have to play a very good game to make sure that we qualify. We know they are a difficult opponent, but we want to qualify.
"It’s important for the players, but also for the fans.”
Southampton's Shane Long looks dejected after the game
A disappointing showing in the Czech Republic means Southampton have won just one of their last five games which will worry Puel going into their game against Everton and former Saints boss Ronald Koeman.
Further games against Arsenal and Crystal Palace are to come before they entertain Hapoel with their lack of goals contributing to their recent struggles.
In their last seven games, Southampton have scored just five goals with Charlie Austin taking the goalscoring burden firmly on his shoulders, which isn't good enough for a side who want to consistently qualify for Europe.
Puel's selection to leave out Austin backfired with Shane Long looking incapable of stepping into the former Queens Park Rangers man's shoes, but a good win against The Toffees would allay fears and be the morale-boosting win to get his side back on track.
Sparta Prague's David Lafata in action with Southampton's Oriol Romeu