Spurs boss Sherwood saw his team suffer a 3-1 first-leg defeat in Thursday night's round-of-16 tie at White Hart Lane.
The Portuguese club were deserving victors on the night but the touchline antics of their manager Jorge Jesus upset Sherwood throughout the match.
Rodrigo gave Benfica a half-time advantage when he stroked home from Ruben Amorim's through-ball, and Luisao then headed in an Amorim corner on 58 minutes to double their lead.
Christian Eriksen brought the hosts back into the game with a well-struck free-kick but another Luisao goal left Spurs with a mountain to climb in next week's second leg in Lisbon.
Jesus, whose team are now unbeaten in 24 matches, showed three fingers to Sherwood after Luisao made it 3-1, antagonising the Spurs boss at the end of a match in which they did not shake hands.
"I thought his team were very good and showed a lot of class - it's just a shame he didn't," Sherwood said.
"In the first two minutes, he was coming over to the fourth official saying I was stepping in his box.
"He doesn't mind himself, does he, to be fair? Waving goodbye like that [with three fingers]? It lacks class. Why would anyone do that?
"He's got a good side, of course he has, but, nah, not for me thank you. I have no intention of speaking to him."
Jesus downplayed the incident, insisting the three-fingered gesture referred to the goalscorer Luisao - despite the fact the Brazilian wears number four.
"I was saying: 'number three, Luisao, number three," he said. "Maybe here in England, the benches are too close together, compared to in Portugal.
"In Portugal, we have more space apart and we can demonstrate ourselves in our own way.
"When at some stage I invaded Tim Sherwood's personal space, he told me to go to mine. He did the same to me. But it was no more than that, it was quite pleasant in the end."
Jesus was not overly concerned if Sherwood had felt disrespected - "that's his own problem if he felt like that" - and insisted Spurs were by no means out of the tie heading into next week's second leg.
"It was not such an easy win, although we scored three goals and that's a big score," he said.
"We did play quite well and efficiently, we did well defensively and scored three great goals. We are at an advantage, but it's only half-time in this game.
"From previous matches, Tottenham have proved they are more dangerous playing away from home than at home."
"We'll have a go [in the second leg], we'll do our best," said Sherwood. "They were better than us, weren't they? They were better than us.
"They had a lot of attacking threat. They weren't great in the first half and they had one shot which went in, a blow, and then we got done on two set-pieces.
"That's a disappointment, but we haven't opened them up. It's a blow."
Sherwood claimed his players lacked character after their 4-0 Premier League defeat at Chelsea last Saturday but had no such criticisms after their performance against Benfica, despite the defeat.
"I've got no problem with the attitude or desire," he added, with a home game against north London rivals Arsenal approaching on Sunday.
"That's what I questioned and asked for, that's what I asked for. We've got to see it over a consistent basis and carry on going so I've got no complaints about that.
"It's just we have to hold our hands up and say they're a class above."