Sofiane Boufal admitted that Fulham gave Southampton a tough challenge despite their 1-0 win at Craven Cottage.
Following a goalless first-half, Michael Obafemi's 57th-minute strike separated the teams on Tuesday to guide Ralph Hasenhuttl's men to the third round of the League Cup.
The result made it two wins in a row for Southampton after grabbing their maiden win of the season against Brighton and Hove Albion last Saturday.
Editors' Picks
Boufal, who was in action for the whole 90 minutes, revealed the pep talk delivered by Hasenhuttl at half-time which was crucial in the victory.