Juan Mata scored the winner in the second half from a free-kick at Old Trafford as the Red Devils notched up their second straight Premier League win.
The result lifted United level on points with fourth-placed Manchester City – although the Citizens do have a game in hand on their bitter local rivals.
And Spanish midfielder Herrera is determined to help the Red Devils continue their improved form in the coming weeks and months.
Speaking to MUTV after Wednesday’s game, Herrera said: “In the Premier League, you never know what can happen in the next game.
“We have to be prudent and we have to be humble, and we have to go now to West Brom who drew yesterday with the leaders in the table, so it won’t be easy. But when you are Man United, you have to learn to win these kind of games.
“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 and that is what we want to do.
“We want to be in the top four and this won’t be easy because our opponents are also tough, but we are Man United and we will fight until the end because we still have a lot to win – three competitions.
“I think we will fight until the end and if our opponents want to beat us they are going to have to fight.”
United now turn their attentions towards their Premier League trip to face West Bromwich Albion at The Hawthorns on Sunday afternoon.
The Red Devils take on Liverpool in the Europa League last 16 on Thursday 10 March.
MORE: The latest football news