Goals from Chloe Kelly and Lauren Hemp saw City cruise into a two-goal lead at the Joie Stadium midway through the second half.
But we had to dig deep to survive a late onslaught from United, who halved the deficit in stoppage time through Nikita Parris.
City held on to claim top spot in Group B though, and Taylor praised the manner in which his players preserved the all-important three points to book our place in the quarter-finals.
He said: “I always look at the performance. Large parts tonight were really good, at times we saw some good play, but what I like about the team now is we don’t give in.
“We never did previously, but what I mean is we seem to have more determination to see things through.
“It’s never going to be easy in a Manchester derby and they worked tremendously hard.
“So, for us to have that understanding that it means a lot to us, and we want to win the competition, we knew we had to win the game tonight.
“The supporters got behind us really well and saw us home. I’m really pleased we achieved our objective.”
City’s breakthrough came just two minutes after the restart at the Joie Stadium, ending what had largely been a cagey affair until that point, despite Kelly striking to post in first half stoppage time.
But the hosts were full value for our lead once the England winger had converted the opener, and the boss was pleased the overall performance on the night.
For Taylor, the objective was simply to gain the result, and he was delighted that City were able to achieve exactly that.
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“I’m obviously really pleased to win, that’s what we wanted,” he reflected.
“We showed great determination at times, it was a feisty game.
“We didn’t start particularly well but spoke about a few things at half-time where we thought we could be better and we started the second half great, scored the goal and controlled large parts.
“When you get 2-0 up in that period you start thinking a bit we should’ve secured it but one eye on this game still, it’s difficult.
“I’m just really pleased, the players showed good determination and drive.
“We scored some quality goals and could’ve scored more, and I liked the fight and determination to see the result through.”
