Kevin de Bruyne's strike was the difference at Stamford Bridge on Saturday evening, but City certainly could have had more as they moved back to the top of the table.
Delph played an unfamiliar role at left-wing-back but impressed in the strong team performance.
'Winning here is huge, massive,' Delph said on City's official website.
'We knew coming in it would be our toughest game yet this season. We had a game plan and we stuck to it and come out with three points.
'It sends out a massive message. We needed to come out on top and there's a massive togetherness in the team.
'We stuck to the game plan. The plan was to stop them on the counter and we did the job down to a tee, so it's happy days.
Delph replaced the injured Benjamin Mendy, who is sidelined until April with a serious knee injury.
'That performance was for our team-mate, Benjamin,' Delph added. 'He sent us a message before the game and we knew we had to do it for him. That win is for you big man.'