However, team-mate Leighton Baines disagreed, pointing out the quality required for the South African's decisive goal just seconds after coming off the bench in the 2-1 win over Hull at Goodison Park.
Pienaar had not played since August 31 because of a hamstring injury and was pencilled in for a comeback next week at Aston Villa but he impressed manager Roberto Martinez so much in training he was drafted in early.
"It was a lucky touch but I'm happy we've got all three points," Pienaar told evertontv.
"After the last seven weeks it was something I've worked hard for and it paid off.
"I thought 'Get a few minutes, get used to the tempo of the game' so to get a goal and get a win as well is something I'm really happy about."
Pienaar will be looking to re-establish his left-sided partnership with Baines which has proved so profitable in the past.
His team-mate was full of praise after seeing him make a welcome goalscoring return.
"It is typical, it shows his importance," said the England left-back.
"It was a great finish. Sometimes when you first come on the pitch your first couple of touches can be off when you've been out for such a long time but he showed his class and guided it into the corner.
"The more people we can get fit the better chance we've got, especially the quality of people like Steven and Kevin.
"It was important to come back with three points after losing (at Manchester City) before the international break so we are back on the right track in that sense."
Mirallas gave Everton an eighth-minute lead with a disputed goal as Gareth Barry, unsighting goalkeeper Allan McGregor, was not only in an offside position as the ball passed him but Tigers boss Steve Bruce was "100 per cent" convinced the on-loan Manchester City midfielder got a touch.
Barry, already riding his luck with a knee-high challenge on Danny Graham which saw the striker carried off on a stretcher, could have been sent off for an over-the-top challenge on Sone Aluko but was only cautioned.
Aluko exacted some revenge by immediately providing the cross for Yannick Sagbo to convert first-time at the near post and Hull were still in the game right up until Pienaar's 57th-minute intervention.
The performance was not the usual fluid, passing performance expected and on several occasions they utilised the long out-ball to striker Romelu Lukaku but Martinez defended his side in that respect.
"You need to understand that Hull wanted to press us high up and we made some good decisions at times," said the Spaniard.
"When you have the power and strength of Romelu you could see Hull were exposed by that ball - it is a good option if teams are brave enough to press us high up because they know we can play from the back.
"That is a good weapon to have but I don't think we did it well enough or picked it at the right time.
"You saw a little bit of too many tired decisions. When you are tired you go through the motions and picking the right option is not as easy as it looks.
"It was a day to find a way to win the game and I am very pleased with that.
"It couldn't be a pretty performance, it had to be a real professional one to get the three points."
Bruce felt his side, whose four-match unbeaten run came to an end, did enough to earn a draw.
"We had enough chances to get something from it and I can't praise them enough," he said,
"We've been to Chelsea, Newcastle, Manchester City and Everton and we couldn't have wished for a more difficult start."
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