Spurs made a poor start as goals from Jay Rodriguez and Adam Lallana put Saints 2-0 up inside half an hour, but Christian Eriksen quickly reduced the arrears.
Eriksen turned in a Roberto Soldado cross to equalise and Gylfi Sigurdsson fired in a terrific winner in stoppage-time, leaving Sherwood delighted after he recently criticised his players for lacking character after a 4-0 defeat at Chelsea.
"We made hard work of it, after going 2-0 down to a good team like Southampton," Sherwood told Sky Sports.
"You know what it took? Guts, character, spirit. I know it's boring but I think it showed that against Chelsea when I had a few things to say, it hasn't done them any harm, because they know how to dig deep and to respond and grind out a result, and that's what they did today."
Sherwood added: "They know now that capitulation is not acceptable. Listen, we ground out enough results last season when Gareth Bale dribbles up the end of the field and scores four late winners.
"But we haven't got Gareth now and we have to find a way. Sometimes the world-class players are not there but you have to find a way to win."
Sigurdsson's late winner leaves Tottenham six points behind fourth-placed Arsenal, who were thrashed 6-0 at Stamford Bridge this weekend, and Sherwood has not given up hope of claiming a Champions League qualification place.
"We will try and do as best we can," he said. "We are going to try and accumulate as many points as we possibly can.
"I think we might be a point behind where we were last year and we pushed Arsenal really close so who knows what could happen. it is squeaky-bum time, time for the men to stand up and get as many points as we can."
Kyle Naughton was at fault for both of Southampton's goals and Sherwood left his vantage point in the stands to bark instructions after Spurs fell 2-0 down, but he was delighted with the attitude shown by his right-back.
Sherwood said: "Kyle Naughton knows he has made two mistakes, and they are probably the first two mistakes he has made all season, but he didn't hide in the second half and wanted to put himself on offer. He will grow massively from this.
"They were schoolboy goals but you have to bounce back and the manner in which we did pleased me.
"It wasn't silky or fantastic, flowing football, but when we fight and work for each other then the quality players show what they can do."
Sherwood also paid tribute to the performance of Soldado, who has been criticised at times this season but impressed against Southampton.
"He worked like a Trojan. He ran around and left nothing on the field, and that will be appreciated by the fans," said Sherwood.