Just a couple of inches were the difference between one point and three for Kieran McKenna's Ipswich side, who were just minutes away from moving out of the relegation zone.
Had Clarke's effort gone in off the post rather than bouncing back, then Ipswich would in all likelihood have made it back-to-back wins and jumped to 16th in the table.
Instead, they stay behind Wolves on goal difference and a point back from Everton, both of whom have played a game fewer than the Tractor Boys.
"We put ourselves in a really good position in the second half," McKenna told Match of the Day. "The two penalties that we conceded were frustrating because they were both breakaways from our attacks.
"We had the better chances in the second half from open play. I think we have learned how to manage games. We've had a good last three performances - Arsenal, Chelsea and Fulham.
"We have been competitive most of the season. Today, maybe we have left a couple of points out there."
Despite the late disappointment, this was a performance that should encourage an Ipswich side who are beginning to look the part following their promotion.
They were relatively comfortable in keeping Fulham's threat at bay in the first half, despite the hosts bossing possession. When the chances to counter-attack did arise, Ipswich looked dangerous.
Delap was a handful as ever and the Szmodics goal was the perfect example of them getting players up in support in the right moments.
Fulham pushed more men forward in trying to get level for the first time, and Ipswich's response to being pegged back was all McKenna could have hoped for.
While there will be disappointment at failing to hold on for the win, the away point could still be a good one come May, and the display pointed to the prospect of a sustained push for a second season back among the elite.