The Paisley side were 4-1 ahead at half-time against top-flight rivals Motherwell but needed a penalty shoot-out to reach the quarter-finals.

They face the winners of Wednesday's replay between Kilmarnock and Aberdeen.

"I'm delighted we're in the quarter-finals, but we will have some serious analysing to do," Goodwin said.

"Right now, it is just sheer relief because it looked as though there was only going to be one winner after it went 4-4."

After Motherwell's Liam Polworth had cancelled out Jon Obika's opener, the Paisley striker added a second before a Peter Hartley own goal and a Sam Foley strike put St Mirren in control.

But, after second-half goals from Tony Watt, Rolando Aarons and Allan Campbell drew the hosts level, St Mirren were fortunate to finish the game all-square before winning on spot kicks.

Goodwin told BBC Scotland it was "maybe a brilliant cup tie from everyone else's point of view" but not for him.

"For the first half, I couldn't have been any happier," he said. "Then, in the second half, Motherwell had nothing to lose and threw absolutely everything at us.

"They were playing four up front and I have to give great credit to Motherwell for that approach. We just could not live with it. So a slight tinge of embarrassment with the second-half performance then obvious relief is the only other emotion."

Goodwin told his players at half-time he expected Motherwell manager Stephen Robinson to go "gung-ho" after the break but admits they were still caught out by their changes.

"We couldn't cope with their shape and I couldn't even tell you what system they were playing in the end," he said. "It looked like a 3-5-2 at the start, but then all of a sudden they had four men up the park.

"But the fact of the matter is we're in the quarter finals of the cup, we're absolutely delighted with that."