Brendan Rodgers will be tormented by the manner in which Liverpool surrendered their first Premier League win under his stewardship. His team had played with great vibrancy but they were undone by the kind of defensive mistake that will fill their manager with intense frustration, just as he might have been tempted to think everything was starting to click into place.

Martin Skrtel was the man waving an apologetic hand and wearing the expression of someone who could scarcely believe his own carelessness. Liverpool were winning 2-1 when the centre-half tried to play the ball back to his goalkeeper, Pepe Reina, and succeeded only in teeing up Carlos Tevez for an equaliser Manchester City had barely deserved. Skrtel had committed the defender's sin of passing the ball from a blind position and Tevez, loitering with intent, nipped in to score in front of the Kop and leave Liverpool with only a solitary point from the first two league games of the Rodgers era.

With Arsenal and Manchester United sandwiching a trip to Sunderland in their next three matches, it is not the start Rodgers would have wanted but this was far from a Liverpool performance to inspire any sense of unease, certainly not in the manner of their 3-0 defeat at West Bromwich. They were the better side for long periods and, though they must feel great exasperation, they can still take encouragement from they way they tackled the champions. If nothing else, it should soothe any lingering nerves from what happened at The Hawthorns.

Liverpool not only played with great industry and togetherness but demonstrated a sense of belief that must have invigorated their crowd. The home side could easily have lost direction after Yaya Touré's equaliser had threatened to turn the game in City's favour after 63 minutes. Instead, the players in red rolled up their sleeves and set about the business of reasserting their authority.

Luis Suárez's wonderfully taken free-kick put them back into the lead within three minutes and, at that point, City looked vulnerable and short of ideas. Roberto Mancini argued that his team had more than matched their opponents, going on to say that not many other sides would create so many chances at Anfield. It was a generous appraisal. City started the game well and might even have snatched a winner during an entertaining second half but the champions looked flat and unusually subdued in other periods. Mancini was experimenting with the 3-4-1-2 formation he tried out in the Community Shield and the conclusion is they are a more potent outfit in their usual 4-2-3-1 system.

There was also the latest sign of possible discord behind the scenes when, losing 1-0, Mancini gave some instructions to James Milner and his player responded with a steam of invective. Too much can be read into these moments sometimes and it is too simplistic to say it represents a lack of team spirit. City have shown on plenty of occasions this is far from the truth. Equally, however, these little outbursts happen too often with this group of players.

Mancini's anger was more focused on his team's marking for the opening goal when Steven Gerrard's corner was delivered with speed and curl and Skrtel attacked the ball in the manner of someone whose only intention was to score. Aleksandar Kolarov, the nearest opponent, was nothing like as decisive and Skrtel's header powered its way beyond Joe Hart. The defender's afternoon would form a wild graph of different emotions.

Liverpool had been threatening City's goal for the previous quarter of an hour and finished the first half on top by some distance. Joe Allen was prominently involved, linking up promisingly with Gerrard. Suárez was joined in attack by Fabio Borini on the right and Raheem Sterling on the left, offering plenty of movement and penetration against the new-look City defence, most surprisingly featuring Kolo Touré ahead of Joleon Lescott.

Sterling justified his selection with some lovely flashes of old-fashioned wing play, although the Premier League can be an unforgiving place for a 17-year-old and the teenager lost Tevez in the buildup to City's first equaliser. Tevez's cross flicked off Skrtel to take the ball away from Reina and, when it came back off Martin Kelly's thigh, Yaya Touré swivelled to score from six yards.

Yaya Touré had just been moved further forward in a tactical switch from Mancini that saw Jack Rodwell come on for the largely ineffective Samir Nasri. Rodwell, as a former Everton player, was baited by the Kop, but it will not have hurt as much as conceding the free-kick that allowed Suárez to score. Rodwell was penalised for a handball when the first connection to block Gerrard's shot was actually with his knee. What cannot be disputed is that Suárez bent the ball around the wall and Hart with great expertise.

Anfield, once again, felt like a happy place but Skrtel's mistake had significant consequences. Tevez missed the injured Sergio Agüero – the same understanding is not there with Mario Balotelli – but he had already turned one effort against the post and was ruthless when given the chance to equalise.

It was his 100th goal in English football and, to Liverpool's anguish, it came wrapped in red and white ribbons.

Man of the match: Joe Allen (Liverpool)