Jurgen Klopp felt Manchester United were fortunate to leave Anfield only trailing 2-0 as Liverpool took firm control of their Europa League last-16 encounter.
Daniel Sturridge gave the Reds the lead from the penalty spot 20 minutes into the first leg on Thursday after Nathaniel Clyne was fouled by Memphis Depay, with Roberto Firmino adding a vital second following Michael Carrick's mistake.
David de Gea made a series of brilliant saves to keep United in the tie, but Louis van Gaal's men face a huge task in the return game at Old Trafford next week.
Klopp joked that his team's performance was "not too bad" and cited chances such as Philippe Coutinho failing to convert from inside the six-yard box as opportunities Liverpool could have taken to add to the score.
"It was not too bad to be honest!" the Liverpool boss told BT Sport.
"We were really good from the first second, everything was there but we could have scored more. That sounds crazy I know but we had the chances.
"In the end, 2-0, if you said this before the game of course I take it. But it's not over, we go to Manchester but it's the best thing we could do.
"Scoring the second goal was very important. We know it is only the first leg but we needed to win it and we did. We are in a good position now, we want to go through to the next round.
"The atmosphere was unbelievable. Really great and I want to say thank you to everyone that was involved. That was Liverpool how I knew it before I came here.
"For us, we had so many difficult situations in this season so now we want to take all we can get for the rest of this season."
Klopp claims he did not see the penalty decision clearly, with contact between Clyne and Depay right on the edge of the penalty area.
"I didn't see it but again I think it was the decision of the assistant," Klopp said.
"It took a few seconds before I heard the whistle, I have to see it again."
Sturridge was replaced by Joe Allen with 25 minutes to go, but Klopp explained it was a tactical decision so Liverpool could change formation to a 4-1-4-1.
"We lost a little bit of control in midfield so we changed system and that's why we brought Joe Allen on," he said.