Although it would not prove enough to progress, Taylor's side defeated the Spanish Champions, becoming the first side to score more than once against the Primera Division side in 38 matches.
Barca had gone 11 games without conceding before their visit to the Academy Stadium and with goals from Janine Beckie and Sam Mewis edging the clash, City scored 25% of the goals the away side had conceded all season.
While a first leg deficit of 3-0 had left his team with a mountain to climb to progress, Taylor asserts he could not have asked for more from his players.
"I was really proud," he told CityTV. "We left everything out there, which is what we asked of them.
"It wasn't quite enough, although at one stage, it looked like it was on.
"We started the game really well but this is the highest level and sometimes, you get punished.
"We knew an away goal would probably kill us and put the tie to bed but up to that point, things looked good and we were gaining opportunities.
"We knew the chances from the first leg would happen again if we did the right things and if we'd have scored a second, it would have given us impetus.
"After their goal went in, I thought the character was top - to be able to carry on and continue fighting, playing our way.
"It was a very good win in difficult circumstances."
The boss also provided an update on Lauren Hemp, who missed the game due to an ear infection, and looked ahead to the rest of the campaign, including the FA WSL title race.
Watch the video above to hear the boss' post-match thoughts...