Chelsea's 1-0 victory over Southampton on Saturday, secured by a brilliant Marcos Alonso free-kick in first-half stoppage time, provided the Blues with their eighth win in 10 Premier League matches.
Conte feels his team deserve greater credit for a run of results that has seen them go joint-second with Manchester United, with City's 15 successive top-flight triumphs for an English record unjustly overshadowing them.
"I think this is not the first time. Alonso is a specialist in this situation," Conte told a post-match news conference.
"There is also Willy [Willian], [Cesc] Fabregas. They are very good. It doesn't matter for me who takes the kicks, but it's important to score.
"I'm very happy for Marcos, I'm very happy for the team. We won a difficult game. I want to remember that in the last 10 games, we won eight games, drew only one game against Liverpool away and lost only one game, at West Ham.
"If someone asks me if I want to sign for this in the next 10 games, I'm ready. Someone is forgetting this run, because there is a team winning every game... My players in the last 10 games did a good job."
Alonso picked up a booking that rules him out of the EFL Cup quarter-final against Bournemouth on Wednesday, while his deputy Davide Zappacosta is ill.
"For sure I prefer to have all my players available, also because we have to play a quarter-final against Bournemouth," Conte added.
"Now there is a problem. Zappacosta is recovering from a bad flu. It can happen. We must be ready to overcome this type of problem. This difficulty."
Southampton's winless run now stands at five Premier League matches but Mauricio Pellegrino felt his side could have departed Stamford Bridge with a point, with substitute Charlie Austin twice being denied by Thibaut Courtois.
"It was a difficult game, especially in the second half. We suffered a lot," Pellegrino told Sky Sports. "When you play with five defenders, you do not have a lot of people in the middle and they managed the ball more.
"We got a couple of chances, we were close but we fought until the end and were close to equalising. The quality of the goal was good, but maybe we can learn more from there.
"In general, the spirit was good and we competed well. It is not easy to have many chances against Chelsea, we had three clear chances but could not score."