Spain striker Roberto Soldado ended his personal goal drought and kept the north London club's fast-fading hopes of a Premier League top-four place alive with the only goal at White Hart Lane on Sunday.
Maximum points helped Sherwood's men consolidate their hold on fifth place, although they remain four points adrift of Manchester City, who lie fourth having played two games fewer.
"It's a huge ask (to make the top four)," Sherwood told Sky Sports. "But it's one we have to believe in. It's more difficult than ever to qualify for the Champions League because there is so much competition at the top end of the table.
"We're looking upwards rather than behind us."
Five of Tottenham's seven top-flight defeats this season have come following Thursday's Europa League football and Sherwood was aware of that beforehand.
The Spurs boss added: "After Europe, as you know our record is poor - very, very poor and it's just about winning ugly at times and I think we did that today."