Sampedro's side sit bottom of the Segunda Division, having lost their last four games, but beat second-tier rivals in the cup to set up Tuesday's third-round tie.
A 1-0 second-round win over Real Zaragoza sent Albacete through and Sampedro will need a similarly strong showing against sixth-place Recreativo.
With just one defeat in the league this term, Recreativo will be strong favourites to progress to the round of 32 but Sampedro is confident his team are capable of progressing to set up a potential high-profile clash with a La Liga side.
"Playing a Primera Division team is not something that happens every day, also the club could have a good box office," he told Marca.
"All have travelled except [Thierry] Moutinho and Diego Benito, and we have held the core of our team and therefore will not change the way we play.
"If we keep playing as we are doing we will have a good campaign."
A number of lower-ranked clubs remain in the competition with Alcoyano, L'Hospitalet, Lleida Esportiu, Cornella and Leioa all plying their trade in the Segunda B.
L'Hospitalet - 17th in Group Three of the third tier - will take on Tercera Division outfit Izarra at home, having taken just one point from their last three league games.
Izarra, meanwhile, are flying high in their Tercera sub-division, three points off top spot having not lost since the opening day of the league season.
Alcoyano are struggling in their Segunda B campaign and are unlikely to be given much chance of pulling off an upset against leaders Lleida Esportiu at the Campo Municipal El Collao.
Cornella welcome Leioa in another third-tier clash, with in-form Group Four leaders UCAM Murcia defending their unbeaten record at home against Real Oviedo.
Eloy Jimenez's side are yet to lose this season and have not conceded a goal in their last five outings, so they should pose a stern test for the former La Liga side on Wednesday.
The Segunda Division's top two meet at the Estadio Municipal Jose Zorrilla, as Real Valladolid welcome leaders Girona, with Huesca and Linense hosting Barakaldo and Cadiz respectively.
Numancia take on Segunda high-fliers Las Palmas at the Estadio de Gran Canaria, with two-time competition winners Real Betis meeting Lugo and Mirandes facing Deportivo Alaves.
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