Jayawardene scored a stylish 85 to play a key role in his team's 243-run Group B win, the second biggest in the tournament history.
Sri Lanka made 321-6 after electing to bat at the Queen's Park Oval here on Thursday, with wicketkeeper-batsman Kumar Sangakkara (76) and Chamara Silva (55 not not) also making merry.
They then bundled Bermuda out for 78, the sixth lowest World Cup score ,with seamers Farveez Maharoof (4-23) and Lasith Malinga (3-10) doing the maximum damage.
"I have not been at my best with the bat in the last two months," said Jayawardene, who had a poor tour of India recently.
"It was good for me to spend more time in the middle. I hope I will continue with it in important games. All the other guys around me are also batting well, so it should be exciting."
Sri Lanka will take on India and Bangladesh in the remaining two group matches, with the top two advancing to the next Super Eight stage.
The Sri Lankan captain was all praise for Lasith Malinga, a fast bowler with a deceptive round-arm action who rocked Bermuda with three early wickets.
"The last six months have been exciting for us, with Lasith around. He has given us more attacking options. He didn't push himself that hard today. He is making his World Cup debut," said Jayawardene.
"He showed a lot of aggression but bowled within himself. He bowled in good areas. The wicket suited his bowling and that was the difference. With his action and the pace he generates, he is always asking questions."
Jayawardene said his team had been looking forward to playing India and Bangladesh in the remaining games.
"Bangladesh are a very good side. They have been in the international arena for quite some time," he said.
"We are definitely looking forward to that challenge. It is going to be tough as three sub-continental sides will play in these conditions, but the World Cup is all about taking those challenges."
Jayawardene also backed Bermuda's participation in the mega one-event, saying the game was a learning experience for them and they were capable of giving better performances in the next two matches.
"We also didn't stretch the West Indies or England in the 1975 World Cup, but we came back strongly to win in 1996," he said.
"There should be a proper development and I'm sure the ICC is monitoring the progress of these countries. The more games they play at this level, the more they will improve.
"For us, it is always good to have these countries playing in big tournaments. That was how we learnt. Hopefully, they will do the same. We have to take into consideration that they are making their debut."