Tunisia have now scored only one goal in nine international matches.
Although their attacking play was often crisp, a combination of poor finishing and bad luck saw Tunisia draw yet another blank.
And Souayah said that conceding two goals in quick succession had meant his team had faced a near impossible task.
"It's true that we held out well for an hour but we conceded
two quick goals against a very strong and experienced Russian
team," he said.
"It was difficult for us to come back."
But despite his side's comfortable win, Russia coach Oleg Romantsev insisted that Tunisia had impressed him.
"I think they have a
good team," he said.
"All they have to do is stop thinking about the score today.
"If they stop doing this and start to relax I think Belgium will have a problem."
Meanwhile, Tunisia's Jaziri sent out a word of comfort for the other teams - Japan and Belgium - in Group H.
"The strong thing about Russia was their short passes and
lots of movement," he said.
"Their physical presence was also quite strong, but with our
technical qualities we could pass through them.
"Their defence was
very slow. It wasn't hard to dribble past them."
"We are disappointed because we played only for victory or a
draw.
"But now we just have to concentrate on making the next match better for us."
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