Eden Hazard cancelled out Sadio Mane's early goal on Sunday, with a dogged Southampton holding on for a point though Chelsea boss Jose Mourinho directed his post-match ire at the officials, accusing referees of launching a "campaign" against his side after Fabregas moment of controversy.
The Spain international was cautioned in the 55th minute at St Mary's Stadium after a challenge by defender Matt Targett inside the penalty area.
Fabregas went over the 19-year-old's leg as Chelsea looked for a winning goal, but his appeals for a spot kick were waved away, and instead he was shown a yellow card for simulation.
Replays suggested that Fabregas had been tripped by an off-balance Targett, and the Spain international joined his manager in criticising the decision, but insisted he would not dwell on the disappointment.
"There was definitely contact," he told the club's official website. "I don't think the referee had the best game of his life but we're all human and a bad day at the office can happen to anyone.
"That's it, let's not talk more about it, we have to talk about football."
Chelsea were perhaps fortunate not to see the dropped points cost them too much as title rivals Manchester City were also held to a draw by Burnley, but Fabregas remains confident the London club have shown enough to demonstrate their credentials.
"If we play like we did in the second half for the rest of the season we will have many, many moments of happiness," he added. "I'm 100 per cent sure of that."
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