Anyway, he was off his game in the first match and Uruguay as a whole were so-so against Egypt, needing a late victor from Jose Gimenez to win by the single goal.
"Of course we demand a lot more from this type of player", Tabarez said at his post-match press conference.
However, while they largely eliminated their defensive errors and enjoyed more possession than their opponents, they were made to pay for one lapse by goalkeeper Mohammed Al Owais, whose misjudgement allowed Suarez to score.
Among the challenges facing Saudi Arabia will be how to contain Luis Suarez, but Al-Jassim does not want to obsess over the influential Uruguay striker.
The World Cup couldn't have begun any differently than it did for Uruguay and Saudi Arabia.
Fernando Muslera had to tip over a long-range drive from Hattan Bahebri, who then missed a fine chance in the box, as Saudi Arabia responded well to falling behind.
The Saudis and Egyptians have yet to collect a point. That puts them in a must-win situation against Uruguay, favourites in Group A. They'll face Egypt in their final group-stage match on Monday, June 25. All the teams out there are good we respect all of them.
Cavani almost made it 2-0 for Uruguay with a solo run through the opposing defence but his attempt was blocked by Saudi Arabia goalkeeper Mohammed Alowais.
"The first game is over and nerves are easing a bit", the Juventus midfielder told reporters.
A first-half goal from Luis Suarez was enough to see off a Saudi Arabia side who seemed determined not to be embarrassed, as they were against Russian Federation last week.
"That was a huge blow to us and I'm proud of how my players came back from it", Pizzi said.