Goalscorer Angelos Charisteas said Greece have earned the right to be taken seriously after their draw against Spain.
Charisteas said: "This shows the Portugal win was not a fluke, and that we are a serious team.
"We will battle in every game because in this competition everyone is nervous and feels the pressure.
"We have played the two group favourites and we have to go on and get a positive result against Russia."
Greece coach Otto Rehhagel challenged his players to grab their chance of making it into the quarter-finals.
He said: "We have a huge opportunity to move into the next stage and the boys must take it."
Rehhagel admitted he gambled in keeping his booked players on the pitch with the pressure from Spain growing.
He said: "I risked it, kept them on and it paid off.
"We wanted to play with the same passion as the win over Portugal but the boys exaggerated and
we quickly ended up with three yellow cards.
"With the second yellow card the heat went up but we took the risk," added Rehhagel after midfielders Costas Katsouranis, Stelios Giannakopoulos and Giorgios Karagounis were all booked within the first half-hour.
Rehhagel also took time out to criticise the black goal nets chosen by the tournament organisers
He added: "They are an absolute catastrophe and could only be the work of some bureaucrat and not some footballer.
"Fans want to see the ball go into the nets, white nets, not these ugly black ones.
"This is not an event where we should mourn, this is a
celebration, and that is all I have to say on this."