Fabian Delph scored the winning goal for the hosts but a series of incidents, including dismissals for Willian, Ramires and Jose Mourinho, marred an entertaining fixture
Jose Mourinho earlier admitted he was left frustrated by his dismissal in the final stages of the game, following on from the red cards handed out to both Ramires and Willian earlier in the half.
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"I think if people are going to comment on decisions, they will do," he said at his press conference after the game. "But I think the football fan and people that are honest will say we deserved to win that game.
"I’m here to talk about the game because that deflects [from the result]. I’m here to talk about football and the good things against a side that cost millions and to do that is a huge, huge effort."
In beating the Blues, Lambert guided his side to their first consecutive victories at home since 2011 and the Scot praised the work-rate of his players against a side he recognised as one of the best in the league.
"I thought we were outstanding, regardless of any decision," he continued. "The decision didn’t change the game. I thought we were worthy of the game.
"I thought the whole team performed outstanding which they had to be as they’re a top, top team - they’re vying to win the league, they’re vying for the Champions League.
"We had to get three points, or try and get three points. I knew it was always going to be tough. We had to do a lot of work and the lads energy levels have totally gone."