"I was apprehensive because you knew that with the final played here on their home ground, that Roma would give everything.
"I was very concerned if we were the only team to go out tonight, that it would have been detrimental to the progress of the team, so it will certainly help us to improve our confidence.
"The team has swum a lot against the stream.
"I believe this kind of result can increase the belief and the self-confidence which can help us for the rest of the season.
Wenger revealed the team had not specifically worked on taking penalties in the build-up to the match.
"I did not think at all it would go to penalties," he added.
"But I had my mind made up in the second period of extra-time who would take the penalties."
Wenger admitted the decision of Spanish referee Mejuto Gonzalez not to award Roma a penalty in the final moments of the first half when Marco Motta and went down under the challenge of Gael Clichy was a "very close call".
"I would like to see it again on the replay. It could have been (a penalty)," said the Arsenal manager.
"Did Gael touch Motta or not? I was worried about that."
Arsenal joined Manchester United, Chelsea and Liverpool in the quarter-finals, as Premier League clubs once again dominate the last eight.
"England can be very proud to have four teams in the quarter-finals for the second year, but we have not to be fooled," said Wenger.
"The games with the three Italian teams - Juventus, Inter and Roma - were very close and it looks like Italy is coming back."
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