Rashford, on loan from Manchester United, sealed the victory with a superb curling strike from a tight angle to take his tally to six goals in all competitions since joining Barcelona in July. The result lifted the defending champions to second in the table on 25 points, five behind leaders Real Madrid after 11 matches.
"When you see the chances he has, I think one or two goals more would be good, also for him," Flick said after the match. "I know he can play at this level and I am happy he is showing it.
"For the fans, the club and his teammates, he is a very important player."
Rashford admitted there was still room for improvement in his decision-making in the final third. "I just try to do the right things on the pitch. Even today, I could have had more assists or goals, sometimes the decision to shoot or pass was wrong," the 28-year-old told Spanish media. "But I will have days like this. The important thing is always the team and today we won.
"My focus is not so much on the numbers. If I do the right things, goals and assists will come."
Barcelona's win was built on a blistering start, with Lamine Yamal and Ferran Torres putting them two up inside 11 minutes.
Rafa Mir pulled one back for Elche before half-time, but Rashford's late strike confirmed the points for Flick's side at Estadi Olimpic Lluis Companys.
Torres praised his teammates' "spirit and intensity" after the victory. "It was important to come out strong, take the lead and play our game," he told DAZN. "We started well, then became a bit complacent, but we found our spirit and intensity again.
"I think we are finding the Barca of last season, who fought for every ball from the first minute."
Barcelona now turn their attention to Wednesday's Champions League trip to Club Brugge before returning to La Liga action against Celta Vigo on Sunday.
Luis Suarez believes Hansi Flick's Barcelona have continued to prove their critics wrong by maintaining their intensity, attacking style and winning mentality under the German manager.
Barcelona have reportedly moved a step closer to balancing their finances ahead of the 2026-27 season after reaching an agreement to sell goalkeeper Inaki Pena to Greek giants Panathinaikos.
Spain manager Luis de la Fuente launched a strong defence of his players after their emphatic 4-0 FIFA World Cup victory over Saudi Arabia, insisting it was "crazy" for anyone to doubt his side following criticism earlier in the tournament.
Spain answered any doubts surrounding their World Cup credentials with an emphatic 4-0 victory over Saudi Arabia on Sunday, as Lamine Yamal and Mikel Oyarzabal starred to move La Roja to the brink of the knockout stages.
