I sat down and worked it out.
In the Scottish Cup, Thistle have beaten a team in a higher league than them on only three occasions in the last twenty years. The most recent was ICT on penalties some 13 years ago, with a replay victory over Premier League Dundee in 2001-02, and a victory over First Division Livingston in 1999-2000. In every one of the 7 seasons we've been in the top-flight, we were eliminated by a Premier League team, with any prior victories against Premier League teams having come on only three occasions (Hamilton in 2014-15, St Mirren in 2015-16 and St Johnstone in 2016-17).
In the League Cup, it's grimmer still. We have beaten precisely two Premier League team in 20 years (Dundee in 2002-03 and St Johnstone in 2017-18, both top-flight seasons). We failed to beat any second-tier teams during our three seasons in the third-tier. During two of our seven top flight campaigns, we were eliminated by second-tier opposition (Falkirk in 2015-16 and Dundee United in 2016-17).
In the Challenge Cup, it's scarcely been respectable either. In just 12 campaigns, we've been knocked out by a team in a league below us on five occasions, the same tier on six occasions, and by a team in a higher tier only once. We have won against someone in the second-tier only four times.
Basically we are fucking shite at cups.