Atletico Madrid climbed to third in the table courtesy of their 1-0 win over Deportivo La Coruna, but it came at a cost as they lost two players to injury
The visitors were reduced to 10 men just before the break when Faycal Fajr picked up a second yellow card, but Simeone's side struggled to break them down until Gameiro replaced Yannick Carrasco on the hour-mark.
The Frenchman subsequently provided the cross from the right which compatriot Antoine Griezmann converted to secure a third league win of the Liga season for the men from the capital.
And Simeone was delighted with the impact made by the summer signing from Sevilla.
"Gameiro's entry was decisive," he said. "Luckily he went well and was decisive in the move that led to the goal.
"He and Griezmann know each other, but they need more time together. Gameiro has just arrived and is integrating into a different style of play.
"But he has talent, speed and can take advantage of small spaces. We hope he will keep growing as a player."
Simeone did concede, however, that Atletico made tough work of seeing off Deportivo, who had lost on each of their previous 10 league visits to the Calderon.
"It took us time to get into the rhythm that was needed," he said.
"The game was complicated and we were forced to make two changes due to injuries in the first half.
"We did not have the pace that we needed in the first half, but played at a higher rate in the second half.
"It was a hard, intense game."
The two injuries that disrupted Atletico in the first half involved Augusto Fernandez and Jose Gimenez who sustained knee ligament damage and a thigh strain respectively.
Augusto looks set for a lengthy spell on the sidelines and Simeone admitted that Gimenez may also miss Wednesday's Champions League clash with Bayern Munich.
"The doctors will inform us better," he said of Augusto. "But it does not look like good news."
On the subject of the Bayern game, the Atletico boss was reluctant to complain about the fact that his side was forced to play on Sunday while fellow-Champions League participants Real Madrid and Barcelona were both handed Saturday fixtures.
Instead he injected some levity into proceedings when insisting that his charges would be ready to tackle the German champions despite the shorter turnaround.
"What we have to do is eat a good plate of pasta and a good homemade creme brulee, and get some sleep," he said.
"We'll do our recovery on Monday, train again on Tuesday, sleep well and then play the game on Wednesday without any excuses."