Tomas Rosicky's stunning goal after just 72 seconds settled the Premier League showdown as Spurs slipped to a third successive defeat following setbacks at the hands of Chelsea and Benfica.
Spurs dominated possession and fired in 17 shots on Wojciech Szczesny's goal, but only two of those were on target as they came up against a determined Gunners rearguard.
And Sherwood, who laid into his players after their heavy defeat to Chelsea last weekend, was significantly more satisfied with their performance, if not the final result.
He told Sky Sports: "I thought we were better than them. I thought we played well and created chances today. We played on the front foot and defended together.
"No-one can say we deserved to lose that game. No-one tries to miss chances, if you're in there to miss them, I can't complain.
"We can't just do that in north London derbies. If the players give me that between now and the end of the season, no problem, we'll be where we need to be.
"The result for Arsenal will paper over a lot of cracks, they were outplayed today and they've got to admit that.
"We've outplayed Arsenal today, and they're title contenders.
"We played better today, a lot better than we have recently. We deserved to win that game, not lose it."
Despite now falling nine points behind their bitter rivals and seven adrift of Manchester City in fourth place, Sherwood is refusing to give up on a top-four finish for his side.
"We've had three defeats, which is obviously very disappointing, but I can't fault them on that performance," he added.
"We just want to try and accumulate as many points as we can between now and the end of the season.
"We go away to Benfica then we've got a big game against Southampton here and we need to bounce back in the Premier League."