Gerrard led by example after the home side was forced to endure Jonjo Shelvey's dismissal minutes before half-time.
Chesting down a loose ball inside the United penalty area, he sent a left-footed volley crashing past Anders Lindegaard for Liverpool's opener.
And the 32-year-old believes a repeat of Sunday's performance against Norwich at the weekend will secure the Reds an all-important first victory.
"We played really well today with 11 men and we played even better with 10," he told Sky Sports. "So we're disappointed to come away from the game with nothing. We showed great determination.
"You can't fault any of the players in our dressing room, they gave everything they had. But sometimes that's not enough against quality teams like Manchester United and they managed to get themselves in front after we took the lead.
"If we keep playing like that and showing that amount of effort and determination, then it will only be a matter of time [before we get our first win].
"If you analyse all of our performances, it's not that we haven't been playing good enough — maybe we just need a bit of luck. We'll keep plugging away and it will come eventually."
"But we know that we need our first win very quickly. It needs to be next week at Norwich."
Prior to Sunday's game, red and white coloured leaflets were raised by the Kop and sections of the Centenary and Anfield Road stands, portraying three simple yet poignant messages: 'The Truth', 'Justice' and '96.'
To commemorate the findings of the Hillsborough Independent Panel's report, the mosaic was held as "You'll Never Walk Alone" rang around Anfield and remained in place for the first minute of the game.
Both sets of players took to the field wearing tracksuit tops with the number 96 printed on the back and Old Trafford ambassador Sir Bobby Charlton presented Liverpool legend Ian Rush with a bouquet of flowers before Gerrard and Ryan Giggs released 96 balloons into the sky.
"I thought it was a nice touch," said Gerrard. "There was a lot said before the game about how the supporters on both sides were going to behave and credit to them both, I thought they were fantastic.
"We're talking about what happened in the game, which is exactly what everyone wanted. So credit to both sets of supporters."