Suarez scored the winning goal in his 100th worldwide appearance for Uruguay, knocking in a corner kick from Carlos Sanchez in the 23rd minute to give the two-time champions a 1-0 victory over the Saudis on Wednesday.
For Mohamed Salah and Co to stay alive in the World Cup, Saudi Arabia will have to win Wednesday night's fixture against the South Americans.
"I do fancy them in this tournament", said Neville.More news: Battle rages for airport in key Yemen aid hub
"We have to fine tune a few things, we have to work on a few aspects".
Egypt's tournament has been a fairytale turned horror story with the injury saga of their key player Mohamed Salah, whereas Morocco played well against Iran and Portugal but were toothless in attack. Suarez has become the first player to score in the World Cup in Uruguay in the World Cup. He fell back to defend and raced forward alongside Edinson Cavani on the counterattack. This just goes to show that fans want good football, boring play styles and a lack of chances really don't go down well, so hopefully, there aren't too many games like this one moving forward! "Undoubtedly there were other factors aside from the pressure of playing in the opening game that made a difference, but it's true that the difference was enormous".
Despite widespread concerns over Russia's quality ahead of the World Cup, the hosts dispatched Saudi Arabia easily on Thursday, running riot over a porous defence to secure a confidence-boosting win.
"Of course we demand a lot more from this type of player", Tabarez said of Suarez at his post-match press conference.More news: Why Didn't Kate Middleton, Prince William Attend His Cousin's Wedding?
The 31-year-old produced a significantly improved display against the Green Falcons and has now scored 52 times for his country, including six goals in 10 World Cup appearances.
"I think two years ago European football took off and they are far away from all the national teams", he said. "That is a cardinal rule for us".
Juan Antonio Pizzi's Saudi Arabia continued to look far more assured on the ball than they did in the 5-0 drubbing by Russian Federation on the opening day of the tournament, with Hatan Bahbri firing a wild volley over shortly after seeing a long-range effort tipped away by Fernando Muslera.
Facing elimination, the Saudis fought hard for a goal with Hatan Bahmi getting several early chances.More news: Switzerland's late victor over Serbia throws World Cup's Group E wide open
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