With the two countries having taken four points from their opening two matches, with healthy goal differences, a draw in Rustenburg will be enough to see both through at the expense of South Africa and France. The hosts and the French meet in Bloemfontein at the same time, but the Mexican boss wants his team to go into the game with the proper mindset.
"If we go out on the pitch with doubts, then we may be inviting defeat," he said. "We can't doubt our ability and I've told my players that. We need those three points and will be going out there to win. They know they have to be fully focused because we still haven't achieved anything, so we have no reason to feel happy."
Aguirre also played down any possibility of the two sides opting for a draw.
He continued: "We're going to try and win. Mathematically we still don't have our ticket to the next round and we have to try and take those three points, so that we can achieve our aims for the first round. The law of the Mexican side is to win. If as a consequence of what happens on the pitch there's a draw or a defeat and we both qualify with no major goal differences, then we'll both be happy. But I can guarantee that the Mexican side is going to go out there to try and win."
The El Tri coach also insisted that his side had the utmost respect for the South Americans. "They are the best and we have to try and beat them. I profoundly respect Oscar Tabarez and his players, who up until now have been the best team in the group. They are extremely powerful, solid and very robust with very talented players. There's not only Diego (Forlan), but others that play in European leagues. But I am highly motivated playing the best and hopefully we can win tomorrow."
Asked whether he felt Mexico could progress beyond the second round - something they have not done since he was a player at the 1986 finals, Aguirre said: "We prepare and look for success. You can't be afraid of taking that step forward." And he feels the current crop of players are amongst the best he can remember, adding: "We have a wonderful generation of extraordinary Mexican players with a very robust mentality.
"We have six or seven illustrious veterans, who have been through the good times and the bad times, but they now feel this winning attitude. But you cannot live in the past, it's all about the present match, each training session. So what we do against Uruguay is what counts, we can't worry about what happened yesterday or the day before."
Uruguay coach Tabarez believes it will be difficult to predict how far his side could go in the tournament. "It would be premature," he said when asked if they could go all the way. "We are ready to play any opponent and in this case it is Mexico. If we do succeed in moving on to the round of 16, and we haven't done that yet, then we know there will be better teams with greater potential than ours."
Like most of the South American teams in South Africa, the two-time champions have impressed so far, following on from their goalless draw with France in the opening match with a 3-0 crushing of the hosts. But Tabarez wants to take things one step at a time, adding: "We feel capable to play any team because it's what we've come here to do. So when we get to that bridge, we'll then cross it. Certainly it's part of our dreams, but for now we are here and will fight to stay here for as long as possible."