Sainz was in second for the first half of the race but after pitting when the pit lane re-opened after marshals recovered Kevin Magnussen's Haas, the Spanish driver was pushed down to eighth position.
Sainz then found himself in sixth when the second restart took place after the red flag, but quickly came through the order to challenge AlphaTauri's Pierre Gasly for the win, coming within four-tenths of the race win.
Seidl affirmed that it was encouraging for McLaren to see the car performing so well on track and that it will help towards further progress up the field in the future, but admitted the first safety car did not help Sainz's progress.
"Definitely that didn't help us because we were in a good position up until that," Seidl explained.
"But, that's how it goes sometimes, we are really happy with P2 and P4 today. Even more happy that we could show we had a really strong car today and it's obviously encouraging.
"We wake up in the morning because we went to win. We know it's not possible at the moment with the performance of the car and where we are at the moment but as I said before, we make steps and that's condition to get to where we want to be in the future."
Despite losing out the AlphaTauri team today, Seidl congratulated the team on their second victory, while also thanking his own team for the job they had done today.
"Congratulations to AlphaTauri and Pierre Gasly for this great win and congratulations to every single member of our team," Seidl said.
"It was a great result for the team. Mixed feelings a bit, but we obviously benefited from the problems Mercedes had so we are really happy, a big thank you to everyone at home also."
Bahrain International Circuit - Winter testing
Would you like to stay up to date with the latest Lewis Hamilton and Formula 1 news from GPtoday? Activate free push notifications and be the first to know!