Morelos forced a stunning save from another excellent Barisic delivery just after the break and Rangers dominated possession for long spells in the second half, showing real confidence on the ball.
The 1-1 draw leaves Rangers tied with Porto on four points, two behind group leaders Young Boys, with two of their final three games at Ibrox.
"I'm very proud of the players," Gerrard said. "The performance was outstanding. We at least deserved to take a point.
"I thought our structure and organisation was brilliant, so I need to pay respect to all my staff who have worked so hard to do that this week. But even more so to the players because they have gone out, they have all maxed out, in and out of possession, and carried out the game plan really well.
"That's the level we need to try and bottle, certainly if we want to get out of this group. That performance gets us something in Feyenoord if we can match that, and the home games will be very important.
"I think that was our best performance in Europe for large parts. If we can find that consistently we'll push this group right to the wire.
"Maybe if Alfredo scored the header and we won 2-1 then for sure it would be the best but I don't want to be sitting here as Rangers manager saying it's our best performance when we have only taken a point. Because we have to remember we are Rangers and we came here to try and win the game."
Gerrard sprung some surprises in his team selection with Filip Helander and Brandon Barker among those coming in but both vindicated their selection. The Swedish defender was arguably man of the match despite the contribution from Barisic and Morelos, who scored his 10th Europa League goal of the season.
"It was a fantastic cross and Buff's composure and finish was world class," Gerrard said.
"I could mention all my players, I thought Filip Helander arrived tonight. He showed the reason why we have so much faith in him and paid the money we did for him.
"It was a performance full of composure and experience, where to be positionally, how to follow runners, how to be switched on, how to manage a game.
"Across the board some really, really strong performances."
Porto manager Sergio Conceciao claimed his side had enough chances, although they only really threatened once in the second half when Allan McGregor pulled off an excellent double save.
Speaking through a translator, Conceciao said: "We had enough situations to win the game, not in a fantastic performance, but we knew that against these teams the quality of the game is lost a lot and the fighting comes up."