season's Champions League, unless they overturn a 2-0 deficit against Olympiakos in Wednesday's last-16 tie and go on to win the trophy.
"It looks like we are a long way off it, we are well aware of that but we are going to keep fighting," said the Scot.
A free-flowing Liverpool could have won by an even bigger margin as they underlined the incredible turnaround in fortunes for English's football's two traditional powerhouses.
They ended last season 28 points behind champions United but are now 14 clear of a side which is virtually the same as the one which claimed a 20th league title last season.
Gerrard's first penalty after 33 minutes followed a deliberate handball by Rafael that could have earned the defender a second yellow card, while his second shortly after the break was for a clumsy Phil Jones challenge on Joe Allen.
Both were converted with ruthless accuracy by Gerrard, one high and one low to the keeper David de Gea's left.
Rooney forced Mignolet into a fine save before halftime as United briefly rallied but both he and Robin van Persie cut isolated figures throughout.
United's day got even worse when Vidic sent Daniel Sturridge sprawling in the area with a lunging tackle and though Gerrard could not beat De Gea again, Suarez's neat finish after 84 minutes capped a dazzling Liverpool display.
Vidic, who joins Inter Milan at the end of the season, now has four red cards against Liverpool, more than any other player against one opponent in the history of the Premier League.
After suffering consecutive setbacks on the road Arsenal revived their own title hopes with only their fourth league win at Tottenham since manager Arsene Wenger took over in 1996.
Despite Rosicky's stunning early blast from 25 metres it was a laboured Arsenal display and they were forced to defend deep for most of the match as Tottenham dominated possession without creating too many chances.
Former Gunner Emmanuel Adebayor and Nacer Chadli both failed to convert presentable chances after the break as Tottenham slumped to a defeat that virtually ends their hopes of challenging for a top-four place.
"Tottenham played very well," Wenger, who will mark his 1,000th game in charge of Arsenal next weekend, said.
"We had an early lead and we were juggling between protecting the lead and finishing the game off.
"It was a must-win game. We maintained the focus to not make the mistake that would cost us."
Chelsea slipped up