Gasly, who joined Renault-owned Alpine at the end of last season from AlphaTauri, qualified fourth at the Circuit de Catalunya on June 3rd but then collected two three-place grid penalties for impeding Formula One rivals.
He ended the race where he started, 10th, after dropping to 14th initially.
"We met in between Spain and here with Pierre and his engineering team," Szafnauer told reporters at the Canadian Grand Prix.
"We met for about an hour-and-a-half to discuss communication strategy, how we communicate with him, the information that he needs, the timing of the information that he gets, what he does with that information, just so we can get a little bit better.
"We have to make sure that when we qualify that high we can actually race there and we will do some things differently, especially on Pierre’s side."
Szafnauer said teammate Esteban Ocon, now in his fourth season at Alpine, was more used to his engineering team than Gasly.
Gasly told reporters on Thursday there had been "small mistakes" made in qualifying which had been reviewed and procedures and communication would be improved.
The Frenchman suffered further misfortune in first practice on Friday when his car halted on the side of the track with what looked like a clutch issue.
Szafnauer said the team, currently fifth in the standings, had been testing the spare steering wheels on both cars to check they worked.
"The rest of the weekend we don't run them unless they are needed as a spare and lo and behold we had an electronics issue within the steering wheel on Pierre's car," he said.
"Once we got it back and put the non-spare wheel on it, it was all OK."