The Reds moved four points behind fourth-placed Chelsea and possess a game in hand.
Speaking to Sky Sports, Phillips described the match as a 'rollercoaster'.
He said: "It was a rollercoaster. It was a strange game. It was an ugly match but we had to make it that way at the end to make sure we got the result. It was a big night for us.
"I think we started quite slow. We knew we still had an extra gear. I didn't feel too worried. It was just a matter of time before we started playing the way we could do. To come from behind is always difficult.
"I reacted too late [to Man Utd's opener]. I thought it was going wide at first then I saw it start to curl inwards. It's one of those things."
On his team's top-four hopes, Phillips added: "It takes us closer. It's another three points. It's no secret what our objective is and that's to win all our remaining games. We can enjoy it tonight but focus is on the next game.
"We can't look away from our camp. We can't have an effect on that. We have to concentrate on doing our jobs. It's something to build on and learn from. We need to take confidence from it."