City were already 3-0 up by that point thanks to a first-half goal from Sergio Aguero and a quickfire burst from Bernardo Silva and Fernandinho in the second half that merely rubber-stamped the inevitable.
Manchester City brushed aside Burnley 5-0 on Saturday but Liverpool kept pace with the champions after Mohamed Salah rediscovered his scoring touch to fire his team to victory against lowly Huddersfield.
"The relationship we had, in that short time, he was always professional", Guardiola said.
Hart conceded five goals to a rampaging Manchester City side, who maintained their unbeaten start to the Premier League season.
The Egypt global came into Saturday's match against Huddersfield with just one goal for Liverpool in his past eight matches but a trademark clinical finish gave him his fourth Premier League goal of the season.
"At 1-0, we're in it a little bit, not massively - they are a top side, nothing I'm saying remotely says we'd have won the game if all this went for us, but it's not helpful when you're playing here against these". "When he doesn't want to be here I think he's not looking forward to coming back here". The performance wasn't 100%. "Every player that is out and comes back makes us stronger".
It was a bitter blow for under-pressure United boss Jose Mourinho, returning to his former club after a poor start to the season and he lost his cool in emotional scenes in the final seconds. That's a mistake, it's the team who build it up from the back.More news: Eagles legend Mike Quick says he's not concerned with Cowboys, Redskins
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"(It was) not celebrations, but bad education.
And on Sane's kick out, Dyche felt that was the easiest decision of the lot: "Then we get on to Sane, which has got to be a red card, for kicking Matt Lowton for no reason at all".
City initially feared that De Bruyne would be out of action until late November, but has good progress and returned to training prior to a 0-0 draw at Liverpool before the worldwide break.
Guardiola said: "I think there is no doubt how important he was and is".
Elsewhere, Cardiff beat Fulham 4-2 to lift themselves off the foot of the table.
The Magpies slumped to the bottom of the league on just two points after losing 1-0 at home to Brighton & Hove Albion, whose day was only marred by an injury to their top striker Glenn Murray.
Brighton striker Glenn Murray was discharged from hospital after being knocked unconscious during the match at Newcastle.