The Liverpool team coach snaked out of Goodison Road with police vans for an escort and irate Evertonians lining the route to bid it adieu. Luis Suárez, not for the first, and in all likelihood not the last time in his career, was the dominant target for opposition derision following his part in the defining act of the 216th Merseyside derby.

Inside Goodison Park, David Moyes had identified his own villain, but it was not the Uruguay international, who doubles as a moth to controversy. Martin Atkinson was the sole focus of the Everton manager's anger following the referee's decision to show Jack Rodwell a straight red card for winning the ball with a clean, one-footed challenge that left Suárez writhing on the floor when the midfielder's trailing knee caught the striker's boot. A finely balanced derby had tilted irrevocably towards an exercise in containment for Everton and patience for Liverpool. For the second successive Saturday, a gruelling afternoon for Everton's defenders brought no reward.

Moyes's team were unable to stifle Manchester City last weekend with a full complement of players for 90 minutes, finally bowing to their opponents' greater resources and stronger bench when Mario Balotelli struck in the 68th minute and James Milner in the 89th. This time it was Kenny Dalglish's introduction of Craig Bellamy that proved instrumental in condemning Everton to a 2-0 reverse. The timing of Liverpool's goals, from Andy Carroll on 71 minutes and Suárez with eight remaining, may have been depressingly familiar to Moyes but the two performances otherwise bore no comparison. At the Etihad Stadium, where Rodwell again played a central role with his limpet-like marking of David Silva, Everton were caged by City's dominance and imagination and offered no real threat of their own. There was nothing between the Merseyside rivals until the perfectly positioned Atkinson drew red.

"It ruined the game," said Moyes. A blunt but accurate appraisal. "There are a lot of questions that people ask about derbies, about tackles, about sending-offs and about players but that wasn't down to a bad tackle by a player. I would have been disappointed if it had been a free-kick and if he had given a yellow card you would have said: 'What is that for?'

"You [the media] want managers to come out and say things but it also needs people who watch and play the game and understand it and write about it to see it because it is easy for me to say it. Too often people talk about the players not doing it right but it wasn't the players today. I don't think anyone in this world thought it was a sending-off but it is one of these things that we just have to take that it was wrong and move on."

Moyes had felt uneasy about Atkinson's appointment all week, not only because they have history. In September last year, when Everton salvaged a stoppage-time 3-3 draw with Manchester United courtesy of two injury-time goals, the same referee had blown up prematurely as Phil Jagielka went in search of a remarkable victory on the counterattack. While the rest of Goodison celebrated the comeback, Moyes and his assistant Steve Round marched on to the pitch to confront Atkinson and berated his time-keeping. The brief stomp cost the pair an £8,000 fine each.

Atkinson and Moyes did not meet again until Tuesday, when the match official arrived at Finch Farm training ground to update Everton's staff on this season's developments and interpretations of the law, a duty he then went on to perform for Liverpool at Melwood. If strong but fair tackles have now been outlawed, Moyes and Rodwell clearly missed the news.

The Everton manager said: "We've not had this referee since myself and Steve Round were fined one year ago against Manchester United. It was interesting that the PGMO [Premier Game Match Officials Ltd] sent him into both clubs this week to do the referee's appraisal prior to this game."

Everton can appeal against Atkinson's decision yet Moyes was unsure if the club would do so. There is unlikely to be such reticence from the Football Association towards the Goodison club after numerous objects were thrown at Suárez in the closing minutes. The Merseyside derby has gained a notorious reputation in recent years and Rodwell was the 20th dismissal in this fixture in the Premier League era, Everton's unlucky 13th. But this can not be portrayed as further evidence of a local spat spiralling out of control or of the underdogs losing composure.

Suárez deservedly won a penalty when clipped by Jagielka and though Tim Howard saved superbly from the usually reliable Dirk Kuyt, Liverpool barely troubled the 10 men until Bellamy's pace and industry told down Everton's right flank. For all the criticism of Atkinson, Moyes did not dispute the outcome.

"The team did everything and I'm so disappointed," he said. "But the referee didn't lose us the game in the end. We made a couple of defensive lapses. It is hard to play Liverpool with 11 men but it became much tougher with 10. At 11 v 11 it wasn't a bad game and we were having our fair share, but the game stopped at that moment."