Despite many people predicting Laurent Blanc’s France would top the section, England overcame Les Bleus to finish first and avoid world and European champions Spain.
With the help of Sweden’s 2-0 victory over the French, Roy Hodgson’s men secured top spot with a gritty 1-0 win over co-hosts Ukraine and Parker admits he was pleased with his team’s performance.
"They [Ukraine] were a good, organised team," Parker told reporters after the game. "Obviously they're good on the counterattack.
"In the hostile environment that it was they put us under pressure at times.
"They had some good chances but I think if there's one thing we've shown during this tournament it's that we've got some good resilience about us. We really dogged it out.
"I think everyone man-for-man stood up and was counted for. The back four were immense and everyone deserves massive credit really.
"The game plan was to win the game. We've won the game and we move on."
Despite revealing his delight at the Three Lions’ display at Euro 2012 thus far, Parker is determined not to rest on his laurels and is aware that the team have only done what was expected of them in qualifying from Group D.
"We've done pretty well,” added Parker. “We realise it's just the start and we move on to the next game now but hopefully we can keep going.”
When asked what he expected of England’s quarter-final clash with Italy Parker replied: "A tough game. A good squad and a good team. We'll go and prepare now. We've obviously got an extra day which is crucial to us."