That feeling was heightened when Ezequiel Garay powered in a first-half header, but Spurs had other ideas and staged a late comeback thanks to a quickfire Nacer Chadli brace.
Aaron Lennon, Gylfi Sigurdsson and Harry Kane all came close to taking the match to extra-time, while the latter had a strong penalty appeal waved away after being bundled over late on.
The match eventually ended 2-2 on the night as Lima scored a stoppage-time spot-kick and, while Tottenham lost 5-3 on aggregate, Sherwood felt the decision not to award his side a penalty cost them a place in the last eight.
"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 goal deserves to go through.
"But for us, the 3,000 travelling fans from London 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 second leg from the Estadio da Luz's directors' box in a bid to avoid another confrontation with Benfica counterpart Jorge 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."
Sherwood was clearly pleased to see the back of Jesus, as well as the three-match losing streak kicked off at Chelsea.
The Spurs boss publicly questioned his players' character after the 4-0 defeat at Stamford Bridge, but had no such complaints in Lisbon.
"People speculated, didn't they? I read a lot of things saying now you need those players on your side," Sherwood said.
"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."
Spurs now return to Barclays Premier League action at 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," manager Jesus said.
"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."
Source : PA
Source: PA