The Gunners went into the Champions League play-off second leg with a one-goal lead following last week's 1-0 home victory but that was erased at the Stadio Friuli in Northeast Italy when Udinese captain Antonio Di Natale headed home six minutes before the break.
But Arsenal responded ten minutes into the second half when Robin van Persie slotted home from six yards after Gervinho had teed him up perfectly and with Di Natale missing a spot-kick prior to the hour-mark, the visitors pounced through Theo Walcott in the 70th minute to win 2-1 on the night and 3-1 in aggregate, allowing them to progress to the group stage of Europe's premier club competition for the 14th straight season.
"(There is) relief of course, we don't want to go out - and pride as well, because we had our backs to the wall and responded very well in the second half," he told ITV1.
"There was only one team in the second half - Wojciech (Szczesny) saved the penalty, which was very generous, but we played a great game tonight.
"It showed that under pressure this team can respond with football, remain calm and composed and try to play like we can. We had a great belief in the way we want to play.
"There are many questions around our club, if we had gone out tonight it would have been much worse. It was important not financially, like many people have said, but more for the fact we want to play at the top level."