Overall the 23-year-old, a January signing from Chelsea, put in an impressive display and Sturridge was pleased with his showing, but ultimately disappointed that seventh-placed Liverpool, who held the lead themselves for only five minutes, could not come away with a victory.
Asked if he thought it was his best performance for Liverpool yet, the England international said: "I'd say so, although I've not been here very long.
"In the first few games I've lacked fitness, but I feel sharp now and I feel like I am playing and training more like myself.
"There is more to come from me, but I was pleased with the performance today [Sunday].
"It was end-to-end stuff, great for the neutral.
"We are gutted, though, to be fair, because I think we should have come out of the game with three points.
"We are disappointed, but I suppose it is a point against a team who are challenging for the title, so we will take that."
Sturridge - who netted with a fierce drive in the 29th minute, six minutes after City's opener - said he and his team-mates had been told by referee Anthony Taylor to continue playing when Dzeko went down.
"From our viewpoint, the referee said to play on - he said not to kick the ball out," the Liverpool forward said.
"It is not our job to kick the ball out. If the referee says to kick it out we will do that, and if he says play on then we'll play on.
"That is what the ref told us to do, we played on and we scored."
Sturridge picked up a booking for diving in the box in the second half following a coming-together with Joleon Lescott, and he denied after the game that he had gone down on purpose.
"I apologised to Joleon," he said.
"It wasn't that I actually dived, I just lost my footing, and I apologised to him, and obviously there is no hard feelings.
"I'm not a player who dives."
Liverpool manager Brendan Rodgers disagreed with Mancini's version of events regarding their first goal.
"The first goal was clear: both bodies get tangled up, Dzeko thinks it's a free-kick but you're talking about a minute or so after (until Liverpool scored)," he said.
"The referee told a couple of players - Daniel Sturridge and Steven Gerrard - to play on which is why they kept going.
"There was one in the second half when Daniel kicked the ball out. There was no injury to Dzeko, it was purely the referee's decision.
"That (the controversy) probably takes it away from what was a great strike from Daniel."
Despite failing to hold on having taken the lead from Gerrard's superb 30-yard dipping volley, Rodgers was pleased with the performance.
He was unhappy with the mistake by Jose Reina that led to City's equaliser, the goalkeeper charging needlessly out to the left edge of his penalty area only to see Aguero turn and drill home from a near impossible angle out near the touchline.
"That was an outstanding performance today [Sunday] coming here, which is notoriously difficult place where it is even difficult to score goals," Rodgers added.
"We were brilliant. The only disappointment is that we were outstanding in our work but mistakes have cost us.
"Aguero's finish for the second was unbelievable but from our perspective we are bitterly disappointed he was in that situation.
"It was a mistake, everyone is clear on that, but I can't fault the players."
There was yet more praise for Gerrard, with Rodgers saying: "It was a brilliant goal from him to beat Joe Hart from that distance.
"I thought his performance was immense."
Rodgers also claimed that Sturridge, who played through until being substituted in stoppage time despite sustaining a leg injury in the first half, which he is set to have a scan on, will not be available for England's midweek friendly with Brazil.
"He got a knock just before half-time on his thigh and he wanted to give it a go in the second half," said the Reds boss.
"I think he will be a doubt for the game on Wednesday, which is unfortunate because he was terrific today.
"His hold-up play, movement and pace was a real threat, and combination with Luis Suarez, Stewart Downing and Jordan Henderson up front was outstanding.
"He is just with the medics at the moment and he will have a chat with our doctors and he will speak with the England set-up.
"They might want to have a look at it but at the moment he is obviously struggling."