No UK airline has made it on to a list of the top 10 European carriers based on more than 90,000 passenger reviews.
Luxembourg's Luxair was ranked number one by customers of online travel firm eDreams, with an average score of 4.11 out of five last year.
It was highly regarded for the cleanliness of its aircraft, in-flight entertainment and cabin crew.
Austrian Airlines took second place with a rating of 4.08, while Swiss International Air Lines was third with 4.06.
Turkish Airlines came top in terms of value for money, while Lufthansa had the most popular check-in service.
The data, released exclusively to the Press Association, suggests that travellers believe British airlines are no match for their European rivals.
Flybe was the highest rated UK carrier in 16th place with an average rating of 3.89 out of five.
British Airways (BA) scored 3.85, putting it in second place in the UK and 18th across Europe, while Monarch's results were rounded to the same score, putting it in 19th.
A recent review by a BA passenger flying from Heathrow to Luxembourg complained about the "outrageous charge" for checking in luggage, while an irate Monarch customer claimed there was "no reason given" for their flight from Rome to Luton being delayed.
Helen Breen, flight specialist at eDreams, said: "Our survey found that many UK airlines have a lot to learn from their European counterparts.
"The fact that no British carrier makes the top 10 should lead to some concern among our native airlines.
"As more and more airlines fly into and out of an ever-increasing number of destinations, consumers have a larger choice than ever. Flybe, BA and Monarch should be watching their European rivals closely."
:: The top 10 airlines in Europe based on reviews left by more than 90,000 eDreams customers last year are:
1. Luxair, Luxembourg
2. Austrian Airlines, Austria
3. Swiss International Air Lines, Switzerland
4. Aegean Airlines, Greece
5. Lufthansa, Germany
6. Turkish Airlines, Turkey
7. Aer Lingus, Ireland
8. SAS, Scandinavia
9. Air Berlin, Germany
10. TAP Portugal, Portugal