The Blues secured a 3-1 victory to advance to the fifth round of the FA Cup in a performance that was regarded as their best of the season so far.
While for Mauricio Pochettino's side the victory keeps their hopes alive of advancing to the latter stages of the competition, Carragher wasn't in the mood for celebrating.
Writing in a column in The Telegraph, Carragher said: "With apologies to Chelsea fans, Aston Villa's midweek defeat in the FA Cup replay is a setback for English football.
"Villa had the ability to go all the way to those Wembley steps.
"Their loss means that it is highly likely the three major domestic honours will again be shared between the same clubs, underlining how difficult it is to emerge from the pack so the trophy engravers are spelling out different names.
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"Since the Premier League was formed in 1992, there have only been three seasons in which the title was not won by Manchester United, Manchester City, Chelsea or Arsenal.
"Over that period, there are only four years in which one of those clubs or Liverpool did not lift the FA Cup.
"The chances of anyone other than those five winning the League Cup have been better, but not lately. The last team outside of the Manchester clubs, Chelsea and Liverpool to win the competition was Swansea City in 2013. By May, it is likely that 80 out of the last 96 major domestic trophies will have been paraded at the same five venues.
"This is a healthy situation for the serial winners, but not for our game. We need more variety in the honours' lists.
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"The reason for that is not just the power and wealth of the 'big five'. Those just below them should have done better."
After beating Aston Villa, Chelsea will face Leeds United for a spot in the FA Cup quarter final.
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With a Carabao Cup final clash with Liverpool coming up too, the Blues will be hoping to secure silverware this term to ease the pressure on Pochettino.
Chelsea are 11th in the Premier League and as a result, qualifying for Europe could hinge on success in one of the domestic cups.