A well-taken first-half strike from Papiss Cisse was enough to separate the two teams at St James' Park in a 1-0 win for the hosts.
But Sherwood, who lost to Stoke City in his first game at the helm, was still able to find positives.
He said: "We didn't play well last week. The 93rd-minute goal from Stoke knocks the stuffing out of you.
"But credit to the boys, we picked ourselves up and dusted ourselves down and, especially in the first half, we were the best team.
"We went in at 1-0 down. Anxiety came in late in the second half. We tried to play too long, too quickly. I told them in there they need to continue to play and mix the game up and stretch teams, go and get it and be brave on the football.
"But I saw signs. This team is not ready to give up. There is plenty of time left.
"People talk it being about guts and desire to get out of relegation zone. They've got that. They showed me that. They need to show quality under pressure. That's what we need to do."
Some of that pressure could be set to come from within, with Sherwood once again reiterating his ambition to notch up at least six wins between now and the end of the season.
"I am ramping up the pressure on them," he added, "I am telling them 'we can't drop any more points.'
"Managers try and take the pressure off. I think Paul Lambert's probably been trying to do that to the guys all season. I'm going to try the other way.
"This is a massive football club with a lot of good people involved in it. The fans are magnificent. I think it's time we turn the pressure valves up already.
"We need six wins to stay in the division. We will do everything we can to try and do that."
Next up for Villa is a home match against West Brom, who moved eight points clear of them with a 1-0 win over Southampton on Saturday.
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