United lacked cohesion against Watford in a match that seemed destined for a goalless draw until Juan Mata's deft free-kick from 25 metres handed the home side back-to-back Premier League wins for the first time since November.
The victory leaves United trailing City on goal difference after their neighbours were beaten 3-0 by Liverpool and Herrera said that by winning without being at their best, the team showed they were ready to fight for a return to the European elite.
"We have to be honest, we didn't play so good," the Spaniard told the club's website (www.manutd.com).
"(But) we are showing passion that we want to fight until the end, and when we don't play good, we still have the belief that we can win.
"We know that a few weeks ago we weren't playing so well and losing matches we shouldn't have lost. We had two options: to either give up, or fight until the end.
"We want to be in the top four. This won't be easy... but we are Man United. If our opponents want to beat us they are going to have to fight."