Spurs again today were booed off at half-time having seen Mohamed Salah scored twice for Liverpool to build up what proved to be an inassignable lead.
Spurs have now lost three in four and defeat to Liverpool saw them drop out of the top four for the first time since August, but Souness says Conte deserves patience from any fan running out of it.
"I think what compounds their problem is there is a team [Arsenal] up the road that’s doing well and they’re being perceived to play a brand of football that’s deemed attractive," Souness told Sky Sports.
"The fact that Arsenal are top of the league, and Spurs are fourth ... they've got the right manager, and with the right support he'll do well at this football club."
Souness continued: "They have some really good players, and they'll do well. Slowly, slowly, don't be critical, let the team evolve, let him get on with his job and support him.
"He alluded to it, I think Harry [Kane] alluded to it [in their pos-match interviews]: I think the support could be better. They are a demanding crowd, they are a big football club and sit in the best football stadium in the world so they feel they should have more.
"If Arsenal were sitting below them right now, they wouldn't be making the same noises."
Conte said after the game that he was disappointed with the fans booing.
"First of all I think we have to show a great respect all the time for our fans," Conte told reporters. "They are our fans and they pay their tickets.
"At the same time, if you ask me if I was a bit disappointed (about the booing), yes. Because it's important in every moment to be honest and I think I always continue to repeat, we have just started a process.
"I think after a year we have made a lot of improvement. If someone thinks after just a year we're ready to win, I say it would be really, really difficult. Liverpool is a really good example that you need time and patience. If we have this everybody is okay. If not, then we can lose our passion and our enthusiasm."