Conte expressed concern this week that Chelsea's record signing could be forced to miss the rest of the season with a mystery back injury.
Speaking after making his home debut for the Blues in their 3-0 win over West Brom, he said: "As a football player you need to move on and be ready from the first day at your new club".
"We need him up and running as it's goals we've struggled with", manager Alan Pardew said after the match they lost to champions Chelsea. The only people who are going to believe we can (survive) is ourselves.
"We started the game with some problems but then after we scored I felt we controlled the game, we created the chances to improve the result".
The Italian was relieved his side put their recent bad spell behind them, adding: "It was very important to get three points and to win the game, especially for the confidence".
"Again we had a big chance at 1-0 when Salomon was through on goal and I think Evans's header was at 1-0".
"It's not easy to lose two games but now we are back", said Hazard.
"My players know very well what our work is and what we have to do. Training is okay but games are better and more important".
Conte had been unable to name a recognised striker in either of those matches with Morata sidelined for almost a month due to a back injury and Giroud having joined from Arsenal only on Jan 31.
Meanwhile, Chelsea were handed a further boost during their win over West Brom with Andreas Christensen returning to Conte's starting line-up following a hamstring injury that had been sustained during the defeat to Bournemouth on 31 January.
"We want to go to the next round (against Hull) then to prepare the game against Barcelona and then United and City".
The guests likewise stay five focuses behind Stoke, the group closest to them in the table, and with 11 fixtures remaining are confronting a fight for survival. "We just couldn't hurt them".