We never upset the odds.. perhaps the longest shot we've achieved are a couple of wins at The Etihad under Moyes - maybe 5/1 or 6/1 - maybe Man U away in 1992 but that wouldn't be such a long shot back then. I can't recall a single result away from home where we've brought in a complete outsider.
We frequently lose at Spurs after taking the lead.. we miss out at Arsenal (2-2), Liverpool (2-2) and others.. not strong enough mentally and a manager (Moyes) who couldn't hack the pressure in almost all big games.
Wolfsburg away was one to be proud of, ditto Nuremburg, Bern and Athens but they were much weaker teams. We didn't get those 2nd leg results against.. Dukla, Panathinaikos, Inter, AC, Sporting, Dunfermline, Man Utd etc (Europe), City, Chelsea (League Cup).. the list is long and painful.. West Brom (1968), FA Cup replays vs Fulham, West Ham (though not Chelsea - penalty win). It's disappointing but that's why we say "Everton that". Hopefully, a few years down the line we'll be thinking about some better ones.