Chelsea manager Antonio Conte experimented with a new formation in Thursday’s 2-1 success at Turf Moor as January signing Giroud was partnered with last summer’s big-money capture Morata.
The pair had played together from the bench, but never from the start, and Giroud was impressed with his link-up with the Spain international.
"We haven't played together much, but it is easy to play with this kind of player," Giroud said at Turf Moor.
"Obviously we have an opportunity in training to work on it and we know exactly what the manager wants from us. We can find each other easily on the pitch because it is easy to play with this player.
"No [competition], not at all. We just played to help the team win the game. I was a bit sad for him because he didn't score. I tried to help him in the first half and in the second half he could have scored as well. I wanted to assist him, but I will do that next time. One thing is sure, when Willian or Eden [Hazard] don't play we just try to give everything for the team.
"I feel very good. I was very tired because this game demanded a lot of pressing from us. The coach wanted us up front to press very high, not let them go inside and pass the ball because it is in this situation where they are the most dangerous. I tried to combine with Alvaro in the first half.
"It was good for me but in the second half it was more on the counter attack. We could have scored more but at the end of the day we are very pleased with this victory. It is never easy to win here."
Morata reacted angrily after being replaced by Hazard in the second half as Giroud completed the full 90 minutes. It is likely that Conte will bring Hazard and Willian back into the team for Sunday’s FA Cup semi-final against Southampton and drop one of the strikers to the bench.
Giroud has been a success in the FA Cup after winning the competition three times with Arsenal and he is hoping that a triumph will Chelsea will be a platform for him to win many more honours.
"If I win it again, it would be my fourth FA Cup in five years. I'm very excited," he added. "It's a competition that is very important for the fans and for us. We are still hoping to qualify for the Champions League and, as long as it's mathematically possible, we still have hope. The FA Cup is something different. Obviously, I want to win it with Chelsea.
"I am not an Arsenal player anymore so my target is to finish as best as I can with Chelsea. Chelsea is a competitor. In the last 13 years, Chelsea have been the biggest club. I signed here to win trophies. Obviously, Manchester City have done very well this season to be champions and that's why it's (the title race) over for this year.
"But I believe we can compete very well next season. I am looking forward to that. But we need to finish the job this season. We are professionals, we are competitors and we will believe until the end."
It looks tough for the west London club to qualify for next season's Champions League but Giroud is keen that his side keep putting the pressure on.
"Yes. We will try to put pressure on Tottenham and Liverpool until the end," he continued. "We know that we have to play Liverpool in the penultimate game. We are going to keep fighting until the end."