In a re-run of last year's final, Bayern made a positive impression against the reigning champions, with Franck Ribery and Arjen Robben both hitting the post before Gomez took advantage of a Julio Cesar error late on.
The away goal leaves Inter with a huge task ahead of the second leg but, having been frustrated by what he considers an unfair result, Sneijder is determined to turn things round in Germany.
"We deserved the victory," he told RAI. "We deserved to win - we played well and created a lot of chances - but the reality is that we lost, even if it's not over yet.
"We all knew they had quality players, especially in attack. We did well - we just lacked goals. In Munich it will be difficult, but it's not over."
Inter boss Leonardo refused to blame his goalkeeper for the result.
"Julio Cesar has no need to apologise," he said. "There were many chances in this game and it's part of the sport. He parried it and the goal could've come in other moves, just as we had the opportunities to score.
"It's true that this loss is even more disappointing because it came right at the end, but it's all wide open for me, as we played on level terms tonight."
Inter's defeat followed home losses for AC Milan and Roma in the Champions League, but Leonardo dismissed suggestions Italy was falling behind other countries.
"Serie A sides remain competitive, as I didn't see any enormous difference and the competition remains very balanced. We'll go to Munich with optimism and the desire to go through."
Bayern boss Louis van Gaal said he had been surprised by Inter's attacking approach during the game.
"It was an entertaining match with many scoring opportunities," he said. "Perhaps we created a few more, so I am satisfied, then at the death we got a bit of luck. I really liked the second-half performance, as Inter worked hard without achieving much and we held possession well.
"Inter surprised me, as they played a very attacking and creative style of football, but our goalkeeper, Thomas Kraft, also had a great game."