Fabregas scored the only goal of the game for the Blues as he helped Chelsea FC notch up their third straight win on the bounce with a 1-0 victory at Swansea City on Saturday lunchtime.
That was enough to secure a third successive league win for Antonio Conte's fifth-place side, which moved within two points of Tottenham, which faces Watford on Monday.
He told BBC Sport: "The only way we can put a bit of pressure on the top four is to win".
"The bad thing is that it's not up to us but we have to be right behind putting pressure because in football, anything can happen and we have to be there to make sure that if it happens we are there to take it". Our live coverage lets you follow all the key moments as they happen.
Andre Ayew and brother Jordan both went close, but a late push for an equaliser went unrewarded to extend the Swans' winless run to six going into their final three fixtures.
"I think even today we could be more clinical to kill the game, but instead we kept the Swansea City vs Chelsea game in balance".
Swansea, meanwhile, are just one point ahead of 18th-placed Southampton following Mark Hughes' side's 2-1 win over Bournemouth earlier in the day.
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The draw left Liverpool needing a maximum of four points from its remaining two matches to guarantee qualification for next season's Champions League via a top-four finish.
The goal flurry came in the last 10 minutes when Ruben Loftus-Cheek and Patrick van Aanholt netted and Christian Benteke struck a penalty.
With an nearly flawless finish to their league campaign needed to overtake either Tottenham or Liverpool, Chelsea will need the former Footballer of the Year to remain as dependable and decisive as he was here.
Swansea were successful in disrupting Chelsea's flow at the start of the second period but, much like in the first-half, they rarely looked like finding an equaliser.
Dusan Tadic breathed new life into Southampton's bid to beat the drop as his double sealed a crucial 2-1 success in the south-coast derby against Bournemouth at St Mary's.
Suddenly, Chelsea looked more vulnerable, but Swansea have struggled to score goals all season.
"When we arrived we were five points away from the teams above", Carvalhal said.
Cherries defender Cook made a mess of McCarthy's long kick and Tadic collected the ball, drove forward and expertly found the bottom left corner from 20 yards.