The forward was put through on goal after nine minutes, with the score at 0-0, but hesitated before losing possession when well placed to score
He demonstrated a similar lack of confidence later on, and was substituted as Saints fell behind
Rodriguez, back making regular appearances having suffered anterior cruciate ligament damage in 2014 and then experiencing several setbacks en route to recovery, spoke of his frustration and belief that he should have scored, but was adamant his fitness was not preventing him from rediscovering top form
"I feel fine, I feel great," the 27-year-old said
"I just want more and more of it
That's what I need and I'm sure the goals will come
I just need to keep my fitness and keep on the field.
"I need regular games
That's the main thing
I need a run of games to find my form and the goals will come.
"It's one if those things, it just happens, but I'm working hard to keep extra fit and I'm sure I will be.
"I cut inside and I should have squared it or taken the shot early
It was just one of those things
I should have decided earlier what I was going to do.
"I'm not happy
I'm always like this after a game if I haven't scored.
"We came here to win and we had the chances to and, although we're disappointed, we can't keep our heads down."
The result meant that Southampton, having hoped to extend their lead at the top of Group K and taken a significant step towards reaching the knockout stage, instead slid from third to fourth.
It also gave Inter their first points of the competition and left the pool wide open when the Italian side - who visit St Mary's in a fortnight - had been at risk of elimination.
Asked about the competitive nature of the group, Rodriguez said: "We know that but we've got home games now and that'll be a strong point for us
We have to focus on the next game.
"It's a proud moment (to play at the San Siro) but it doesn't really mean anything when you lose
We have to now focus on (the Manchester City fixture) on Sunday."
Source : PA
Source: PA