The Spanish winger was a shining light for the Toffees who came from two goals down to eventually defeat the Tykes 5-3 in the second round of the Capital One Cup at Oakwell.
Deulofeu provided crosses for Steven Naismith's 59th minute equaliser and Romelu Lukaku's 78th minute leveller in the topsy turvy affair before sending in a ball which Marc Roberts saw into his own net which allowed the visitors to take a 4-3 lead before Lukaku's late finish.
"He was outstanding when he came on," said Martinez on the club's official website.
"His pace, penetration and ability in one-v-one situations was something that inspired our second-half performance.
"As you could see at the end, he was finding it tough. The plan was never that he would play anything longer than 45 minutes. But he adapted well and can only benefit from it.
"It was a really good display. But everyone in the second half, individually and collectively, was very strong. It would have been all too easy to let the momentum of the first half contaminate the second, but the attitude of the team was very clear – we wanted to get through. It was tough but we deserved it."