Memphis Depay scored the only goal of the game from the penalty spot in the second half at Camp Nou as Barca ended a four-game winless streak in LaLiga to climb to sixth in the table.
Just over 74,000 fans attended the game, double the amount that attended Barca's last home game against Alaves, but they almost witnessed a sting in the tale as Espanyol missed a flurry of late chances.
"In general, I was happy with the performance and the three points," Xavi, who replaced Ronald Koeman earlier this month, said in his post-game news conference.
"The attitude and the effort were very good. We dominated for 75 minutes but from there Espanyol created a lot of problems. We had some luck with the woodwork twice.
"It's difficult to attack a back five with a line of four in front of them, but we have to work on that because we will come up against it many times.
"We need to take more risks going forward but that comes with confidence and time. We need to know when to go wide and when to come inside and we need to work on our timing. I'm happy but there's a lot to improve."
Xavi said Barca's sluggish final 15 minutes was "not a physical problem but a football one" and called on his players to "keep possession and show more personality" moving forward when protecting leads.
However, it was the "exceptional" Abde Ezzalzouli, 19, whose performance most caught Xavi's eye after coming on for Ilias on the left of a front three at half-time.
Espanyol were aggrieved to leave with nothing. Striker De Tomas, who hit the post twice, said the penalty, given for a Leandro Cabrera foul on Memphis, was a "joke," while coach Vicente Moreno also felt the decision changed the game.
"That was a key moment," Moreno said in a news conference. "If we take away that, I think we were maturing into the game at that point."
Prior to the match, reports had emerged suggesting a heart problem has forced Barcelona striker Sergio Aguero to retire the game.
Sources at the Catalan club told ESPN that was not true and referred to a statement released after the Alaves game in September, when Aguero experienced chest pain, which said he would be treated and monitored for the next three months.
"What has come out about Aguero is not true," Xavi added. "I spoke with him the other day. We will see how things evolve and if he can continue playing football, but it's a medical issue."