The Premier League side fought for a 2-2 draw at the Estadio da Luz on Thursday, but a 5-3 aggregate defeat saw them fail to reach the UEFA Europa League quarter-finals.
Sherwood had asked for a response from his team after three straight losses, including a 4-0 defeat at Chelsea which led to him questioning their character.
But he believes the performance in Portugal was an indication that his rant post the Chelsea loss did no harm.
"It's evident the players are on my side. My little rant has done them no harm," Sherwood said.
"They have showed character and guts and they need to do that until the end of the season and I'm confident they will do that."
Benfica took a 3-1 lead into the second leg and extended in on 34 minutes through Ezequiel Gray's header.
Nacer Chadli scored twice in as many minutes in the second half to drag the visitors back into the tie, but Lima sealed the result for Benfica with a late penalty.
Sherwood, who chose to sit in the stands after his first-leg confrontation with Benfica coach Jorge Jesus, was pleased to see his opposition number under pressure.
"We had them where we wanted them. They were running scared," he said.
"It was good to see their manager sweating as much as he did. I didn't see a suave character, he looked really flustered. It was worth the entrance fee to see that.
"The team who scores most deserves to go through but the 3,000 Tottenham supporters must be proud of what they saw.
"They stuck behind us and travelled in numbers and likewise the boys put on a performance which they can be proud of."
Sherwood felt Tottenham should have been awarded a late penalty which may have forced the tie into extra-time after Harry Kane appeared to be pushed by Benfica defender Miralem Sulejmani.
"Sometimes you get them and sometimes you don't and at the moment we're not getting them," he said.
"I think we would have gone on to win it. We had them where we wanted them."
