Spurs bowed out of the tournament at the last-16 stage after drawing 2-2 at the Estadio da Luz on the night, having lost the first leg 3-1 in north London last week.
However, the visitors came close to causing a major upset in Lisbon. Having fallen behind to Ezequiel Garay's first-half header, they turned the scoreline around after Nacer Chadli's quickfire double and had a strong penalty appeal turned down in the 88th minute.
The Portuguese giants were eventually awarded a spot-kick of their own in stoppage time, which Lima won and converted, and went through to Friday's quarter-final draw 5-3 on aggregate.
At least the result ensured Spurs avoided a fourth straight defeat for the first time in over 10 years.
Sherwood had publicly questioned his players' character after the 4-0 defeat to Chelsea at Stamford Bridge on March 8, but had no such complaints on Thursday night.
"People speculated, didn't they?" said the Spurs boss. "I read a lot of things saying now you need those players on your side.
"I think it's evident they're on my side and the side of the club. They fight for the cause and my little rant, if you want to call it one, has done them no harm.
"They have showed real character and real guts and they need to do that until the end of the season, because we've got some tough games ahead and I'm confident they will do that."
Benfica may have eventually extended their unbeaten run to 26 games, but Sherwood - who was without 11 first-team players - felt his players had Jorge Jesus' side on the rack, and particularly rued Slovenian referee Damir Skomina's decision not to punish Miralem Sulejmani's challenge on Harry Kane in the box late on.
"Sometimes you get them and sometimes you don't and at the moment, we're not getting them," the Spurs boss said.
"We had them where we wanted them. They were running scared, weren't they?
"It was good to see their manager sweating. I did not see a suave character on the side, I thought someone who was really flustered, which was good to see.
"That is what we intended to do and that is what we achieved.
"Credit to Benfica, they go through over two legs. You have to say the one that scores the most goals deserves to go through.
"But for us, the 3,000 travelling fans must be proud of what they saw.
"The boys are very proud about what the fans have done for them tonight as they stuck behind them, travelling in numbers, and the boys have put on a performance which they can go and be proud of."
Sherwood swapped his gilet for a suit and tie to watch the action from the directors' box in a bid to avoid another confrontation with Jesus.
The pair quarrelled throughout last week's match, which ended in them not shaking hands after the Portuguese showed the Spurs boss three fingers after Luisao made it 3-1.
"I just wanted to get a better view up there and maybe take some steam out of the situation," Sherwood said. "It was about what our boys could do against their boys on the pitch.
"Obviously there was a flare-up between me and their manager last week and I didn't want that to take away from what we did on the pitch.
"The concentration was on the pitch and we played better than them.
"Congratulations to him, he's got the chance to wave his fingers at a few more managers in this competition."
Spurs now return to Premier League action on Sunday at home to Southampton, while Benfica continue their charge for a first Portuguese league title since 2010 fresh from a scare on home turf.
"We knew Tottenham could do what we did in London," said Jesus.
"We had five players not used to playing 90 minutes, but it was a risk we took because our objective is to win the championship.
"But we want to go as far as we can in this competition."