Overcoming the Portuguese giants on Thursday was always going to be a big task, having lost the first leg of their last-16 tie 3-1 and after being forced to travel to Lisbon without 11 unavailable first-team squad members.
Such a paucity of options meant it was hard to see Spurs avoiding a mauling at the Estadio da Luz, yet they were unfortunate not to win.
Having gone down on the night to a Ezequiel Garay header, a quickfire Nacer Chadli double led to a frantic final 10 minutes in which Aaron Lennon, Gylfi Sigurdsson and Kane all went close to taking the tie to extra-time.
Spurs boss Sherwood believes the latter should have had a penalty after being taken down in the box, although those appeals came to nothing and the match eventually ended 2-2 on the night as Lima scored a stoppage-time spot-kick.
"I think the third goal at home was a poor goal to give away and it was always going to be a tough ask getting three goals here," Kane said.
"But once we went 1-0 down nothing changed as we still needed to get three goals. We got the two and I think we were very unlucky not to get the third.
"I would say overall the boys were different class."
While Spurs suffered a 5-3 aggregate defeat, they returned from Portugal with renewed optimism after ending a three-match losing streak that began at Chelsea.
Sherwood questioned his players' character after that 4-0 defeat at Stamford Bridge, but Kane believes they showed their true mettle in the draw at Benfica.
"Once we got one and then two they started to get a bit nervous and it was down to us," he said.
"We had a few crosses, a couple of unlucky headers but they are the fine margins in this competition.
"We were playing a great side in Benfica and I thought we were a bit unlucky.
"We showed we are a team and that we are together. We stuck together throughout both legs and hung in there.
"We're disappointed, we came so close. The lads are proud of each other, we feel for each other because we all put in a shift, but that's football sometimes."
Kane, along with along with fellow youngsters Nabil Bentaleb and Zeki Fryers, impressed at the Estadio da Luz, where he outshone the ineffective Roberto Soldado.
The 20-year-old Kane replaced the £26million forward in the 71st minute and there may well be a case to start him in Sunday's return to league action against Southampton.
"The lads were working hard [before I came on] but then perhaps Benfica got tired," Kane said of his impact.
"I posed an aerial threat, won a few flick-ons and got them going the other way a bit.
"We got the two goals and were unfortunate not to get a third in the end."