Magath celebrated his first away win since taking charge of the Cottagers as goals from Kieran Richardson and Hugo Rodallega earned them a 2-1 triumph at Villa Park.
He said: "It was very important we won here after losing our last home game. I think today was our last chance for us to stay in the league. Therefore, it was a very difficult game and very spectacular.
"We were one goal in front, there was an equaliser, and that was the situation last week that put us down. Today we came back and we fought.
"Even the great chance for Lewis Holtby didn't stop us. For us to win in the last five minutes is a signal to everybody that we are back in the league. Everyone at the game could see we want to stay in this league.
"We have to win our games now. It doesn't matter which team we play. We need to win three of the last games at least to stay in the league. We will fight every game. Today we have won and this win will give us confidence."
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