Jean-Philippe Mateta’s late equaliser to cancel out a Chelsea opener scored by Cole Palmer earned Palace the point.
“We are really happy because it’s always good to compete against this type of team,” Lacroix told Premier League Productions.
“We saw a good team of Crystal Palace today. We showed we could be dangerous against them. It’s always difficult to play against us here especially.
“I think it’s not only me, it’s all the team – we defended together. When we are together, it’s always better. We saw in the second-half they didn’t have a lot of chances – they shot one time on target – so for us, we did our job. It’s good for us.
“I think sometimes we respect this type of team – the big teams – too much. This is what we said after. We said: ‘come, we play, we have to win duels, we have to show we have the quality to beat them’ – and that’s what we did the second-half. We deserved it.”